In reading about SLS, I learned that the reason they won't reuse their rocket is that the weight of the parachutes to enable recovery is too much of a sacrifice. How is the weight of the hardware and fuel NOT too much of a sacrifice for Falcon 9?
The top-level answer, as others said, is "because it was decided so".
But following that, we have actual design decisions that simply make SLS completely impractical to recover. It focuses on getting the big payload to a high orbit, and through ignoring the necessity for reusability, it follows design principles that make recovery completely impractical.
The SRBs of SLS could be reused, but there's little benefit in that - they are cheap, simple devices and once the fuel has burned there's really little left to recover - a big, hard shell and some avionics. It never saved much money in case of the Shuttle, and the recovery and refurbishing process was costly and complex enough that it was deemed it's not worth the headaches.
Then there's the core stage. A huge, orange tank of cryofuels and four advanced engines. It would be worth to recover these engines, but it's not possible. The tank is actually quite soft, mostly made of foam with a thin aluminum lining. It carries a lot of fuel, meaning a lot of delta-V. That means it reaches a very high speed and very high altitude. And then it needs to lose that speed and altitude if it's to be recovered.
This is quite opposite to Falcon 9's recoverable first stage, which barely reaches barely 1.5km/s (out of needed 8) and only shortly dips above the atmosphere.
Falcon 9 can brake and descend at reasonable, survivable speed, without burning up and without spending excessive amounts of fuel on braking, not to burn up. The second, non-recoverable stage carries most of the responsibility for reaching the orbital speed.
OTOH, SLS core stage pretty much reaches the orbit. It would take enormous amount of energy to slow it down - or some extremely complex (and probably very heavy) technical solutions to make it survive the descent and use air to brake. It's not worth the trade-off. It would either need to be even bigger, or it would need to sacrifice a lot of payload weight to survive reentry from that speed. F9's first stage doesn't speed up a lot, so it can be slowed down quite easily. SLS gets so fast, that slowing it down in a controlled way is simply too much effort and cost to bother.
The SLS was designed to be a backstop to replace the Shuttle in the near term, and to support missions to Mars in the longer term. Reusability was not on the agenda then.
Falcon 9 is a step in Elon Musk's vision of enabling self sustaining human civilization of Mars. So his underlying design philosophy is different: it's more long term. This is explained by Musk himself, in a One on One interview video previously posted by user flangford.
Musk's view is that to land anywhere except Earth requires rocket powered soft landings, so SpaceX had better become good at them. Also he believes that competition will drive prices down, making space more accessible. Reuse is a key component of this, so implementing a feature now that will be needed eventually anyway serves both purposes.
According to SpaceX an F9 launch is currently priced at \$61.2M, delivering 13,150kg to LEO at \$4654/kg. In this 2013 answer PearsonArtPhoto quotes Falcon 9 at \$4,109, Ariane 5 at \$10,476, Delta IV at \$13,072, and Atlas V at $13,182. In round numbers SpaceX is quoting 30-40% of the price of other Western launchers.
But the price competition gets stronger with Falcon Heavy. The same SpaceX page quotes a Falcon Heavy launch at \$85M, delivering 53,000kg to LEO at \$1604/kg, 1/8th the cost by a Delta IV (and also comparing 2013 dollars to 2015 dollars).
In the video Musk also mentions that SpaceX is planning a bigger vehicle to follow Falcon Heavy.
The difference is due to completely different design objectives, driven by different corporate philosophies. Competition between launch systems is expected to drive costs down, and as costs drop then more missions will become practical, leading to an expansion of the launch market. In the SpaceX view, reuse is key.
SpaceX has decided that reusability is a critically important goal to keep long-term costs down, therefore they've designed in the ~15%-30% performance margin they need to achieve reusability (the lower figure for mid-Atlantic barge landing; the higher figure for boost-back to the launch site). Cost is critical for SpaceX because Falcon 9 has to compete commercially with other medium-lift boosters like Delta IV, Atlas V, and Soyuz. If they achieve the reusability they hope to, the increased cost of a 15% more powerful booster will be more than covered.
SLS is a much bigger rocket, carrying 5-10 times the payload. The only launches that really require that are manned missions beyond LEO. Such missions are few and far between and don't have to be cost-effective in the same way that a communications satellite launch has to be.
Falcon 9's reusability plan is based on precision powered vertical landing. SLS's core stage is much larger and heavier, and landing it in a similar way would be a substantially harder problem. Parachute landings would probably be feasible, but that makes recovery and refurbishment more time-consuming and difficult.
The initial SpaceX plan for recovering a first stage was parachutes, into the water. After all they had tons of data available from NASA on SRB recoveries (266 of them?).
But after the tried on the first few flights of the Falcon 9 1.0 they realized they needed to slow the rocket down, before it hit atmosphere (where parachutes would work) or else they got too hot on the way down and burned up.
They took the lessons learned from the Falcon 9 v1.0 and rolled them into the Falcon 9 v1.1 which is what you see launching today. (Of course, they have since added grid fins, changed the amount of control fluid for those fins, are about to uprate the Merlin 1D engine in the next few flights, and probably many more changes they won't tell us about).
That should give you a pattern on how they approached reuse.
SLS is planning on launching payloads once every 4 years if we are lucky. It is unlikely they will be willing to experiment, learn, react, and update the same way in that kind of a model.
When SLS was designed, recovery was not considered a priority. So while in the Shuttle days, the SRB's were at least recovered, and mostly reused (after a LOT of rework, to the point, there was almost no cost savings) for SLS they are being thrown away, no attempts at recovery.
Whereas the SSME (RS-25D engines) that the Shuttle used could be reused (after significant and expensive refurbishment work) the SLS will not be recovering them, instead throwing them away.
I am known to be cynical about SLS in this aspect, so take my perspective with that grain of salt, as I suggest that cost effectiveness was never a concern for SLS, only the number of jobs it would maintain in crucial states. (I think NASA is a great research organization. I think they are a terrible launch provider. Big difference.)
If you consider that versus the SpaceX model of trying to make money, and in the process bring launch dominance back to the US, increase humanities presence in space then it is obvious why.
They are placing their bets differently
While SpaceX is quite innovative with their reusable launch system, NASA has a more conservative approach and builds a fully expendable launch system because that's what has proven to work.
After several failures, SpaceX managed to pull it off and fly the first stage back to the launchpad. But if this feat can be replicated reliably and if it is actually cheaper is still open. So the future will tell us which approach will prevail.
Also, the SLS is trying to break the record for the most powerful launch system ever built. A fully expendable system will always be more powerful than a reusable one with the same launch-mass because you don't need any landing equipment and no part needs to be built more sturdy than required to survive just a single launch.
In reading about SLS, I learned that the reason they won't reuse their rocket is that the weight of the parachutes to enable recovery is too much of a sacrifice.
More like, it's impossible to build parachutes big enough to slow it down enough to survive impact. The SRBs on STS used the biggest parachutes ever made, and they still hit the water hard enough to cause significant damage. SRBs are pretty robust vs. liquid fuel tanks and engines. Even if you could make parachutes big enough to enable a splashdown of the SLS core, the tanks and engines would be smashed by the impact.
Not to mention dunking hot rocket engines in cold salt water would probably render them non-reusable, even if they managed not to be destroyed by the impact.
When SpaceX was developing its reusability technology, the first few stages went into the drink, where they promptly broke apart and sank due to wave action. SLS is a lot fatter for its length than F9, so it might be a little more robust in that respect, but you'd still lose the engines which is the one thing you really want to recover and reuse.
But the simple answer is that reuse was not a design consideration for SLS. At all. It's designed to loft very heavy payloads while keeping certain contractors employed. In fact, with its proposed flight rate (1 every other year), spending the extra money to develop a reusable system doesn't make that much sense. Reusability makes sense for SpaceX because they have dozens of missions waiting for a ride right now, and potentially hundreds with their satellite constellation plans. Even if it only saves them a million here or there to use a pre-flown booster instead of building a new one, over the number of missions they have planned that adds up to real money.