Why is Soyuz the only spacecraft that sends humans to the International Space Station and we don't use any other spacecraft?
Why do we only use Soyuz to send humans to the ISS?
Because other than Chinese spacecraft (which aren't allowed), the Soyuz is currently the only one that can send humans to the International Space Station. The only other vehicle capable of carrying humans to the ISS, the Space Shuttle, was cancelled. That metric (no other vehicle can do it) will hopefully change sometime soon. NASA has contracts with SpaceX and with Boeing to develop vehicles capable of transporting humans to the ISS.
The main reason why there are no alternatives to the Soyuz launch system is the phrase "Why pay more?" raised in '90. Most of the new space launch systems in development were canceled (including Hermes of ESA for example) in a favor of already existing ones. Those days Russia was selling a seat for \$20M, but now it's 5-10 times more expensive (due to the monopoly). ESA paid 200M € for the French astronaut for example. Now everybody is back in design and development. Unfortunately the process is very expensive as well as very slow, mostly because of a very low demand for these systems — the automotive industry as well as an electronic one are way more profitable. Also insurance, for example, will cost a huge fraction of the launch cost until there are more than 100 successful deliveries per system, etc.