I read in this article that NASA is building its own rocket for the moon mission.
Why would they build their outdated and inefficient rocket, when they could instead use a SpaceX rocket and use their time to help with that production or do other stuff?
In the defense of NASA, SpaceX does not per se have an operational vehicle for the purposes they want to use SLS. (Yet, Starship is coming)
However, missions to the moon using Falcon Heavy vehicles have been proposed by Bob Zubrin.
Once SpaceX has an actual flying Starship/Super Heavy I think the situation will change.
Ultimately the SLS program is about keeping some of the jobs from the Shuttle program (20,000+) continuing on the SLS project. Be nice to actually launch once, but that may not be critical path to success. (This is my opinion, and cynical)
Because there are no super heavy-lift launch vehicles flying right now. In fact, simply by existing, SLS will be the most up-to-date and the most efficient super heavy-lift launch vehicle since the Saturn V (Shuttle is debatable). Super heavy-lift launch vehicle, Proposed designs
When looking at current SpaceX rockets, the Falcon Heavy are human certified. With a commercial crew, the Atlas V will be certified to launch Starliner, and the Falcon 9 the Dragon 2 capsule. US ready for human spaceflight launch by 2018
Neither capsule can provide for a human crew for deep space travel, to the moon or to Mars. For that, they would have to use Orion, a 26.5 MT vehicle that is tested and ready to go. Neither the Falcon 9 or Falcon Heavy can put 26 MT to TLI. If they were to develop a human certified variant of the Falcon Heavy, then they may be able to do so (after years of additional qualification and testing). Elon Musk has stated he has no plans to develop the Falcon Heavy for crew. SpaceX no longer planning crewed missions on Falcon Heavy
So all current SpaceX launch vehicles are out of the running.
Now, we can talk about Starship. Starship has no launch abort system. Without one, I can very confidently say it will never launch NASA crew. It has no flight hardware, and with two consecutive explosive tank failures, is not as far along as people imagine in their heads. Compared to Artemis 1 hardware, it is incredibly unwise to believe that Starship will launch crew before SLS. Hardware for the first three Artemis missions
Then we can imagine fairy tales where the lovely Starship massively outperforms SLS because of NASA/Boeing's gross incompetence (of which there is a lot). Why not New Glenn? Long March? Etc. Why does SpaceX have to be the contractor, Starship the vehicle, or the US the country?
This question could be edited to produce non-biased answers more openly and start better conversations. The top level question "why is NASA using its own rocket ... Could use SpaceX?" is fine. The detailed one with "outdated" and "use their time to help production" is problematic.
SLS has been in development for a long time, although it suffers from political winds quite a bit. It started in its current form in 2011, when there was no other system in existence that even was close. Falcon Heavy was a concept then, but it would have only been slightly better than Delta IV Heavy, still nothing compared to SLS. They considered other alternatives, but determined that the best thing was to just create their own heavy launch vehicle, and not do a heavy piecemealed approach that was proposed by some.
It's easy to say with at least 3 heavy-lift, and one super-heavy lift, vehicle in development or recently launched that it seems silly to consider any other idea. The fact remains, only Starship is as capable as SLS is theoretically, and only then if you can get it to refill on orbit, otherwise you are better off using SLS. Starship will probably surpass SLS eventually, but it is still a concept. Remember that in 2011, Falcon Heavy was supposed to launch in 2013, and didn't launch until 2018.
Another thing of some consideration is that Orion can't actually launch on a Falcon Heavy directly to the Moon. It's easy to say that you could do two launches, and with some work, it probably could be done to get the payload to the Moon, but in the current form, it just isn't quite workable.
NASA needs to push something forward, and the political winds have dictated using SLS as the rocket of choice. It does make sense for now, but will make much less sense once Starship is launching regularly.
Bottom line: In theory Falcon Heavy, or New Glenn could be used to fulfill SLS's mission, but they are still not quite as capable as SLS, so a complete redesign of the architecture would be required to use one of these rockets. And unless both of them was available, then NASA needs to have their own system to have some means of redundancy.
Another answer not yet explicitly listed could be: to limit the loss of-/build/maintain/expand their independence on other parties when it comes to launch technology (usage). For example, an agency might account for uncertainties in the availability of the technology provided by other parties, or contracts might be such that it becomes difficult/inefficient to continue development on the dependent technologies after use.
This is not saying nor suggesting that this is the case, merely stating that it might be a reason why an agency, such as for example NASA, could opt to develop their own rocket/launcher technology rather than use another, available one. A rationale, tending towards opposite, might be equally/more/less valid, where for long term availability of technology, an agency might want to stimulate other parties in their launcher technology development.
