Why wasn't the US in the League of Nations?

For the same reason that no other countries were in it either. It didn't exist until after the war ended. The League of Nations is a consequence of the Treaty of Versailles and started in 1920.

If you're asking why the US never joined it, that was an expression of the US traditional policy of non-intervention, that the country does not get involved in other countries' squabbles. This has been around for a long time - it's part of the Monroe Doctrine. It also explains why the US didn't join in either of the World Wars until a late stage when it felt threatened itself - or as in the case of WWII, the US itself was attacked.

Rather ironic when you consider that President Wilson was one of the big noises in creating the League. However, when the Treaty of Versailles came before the Senate, with part of it being about creating the League, the Senate voted against. That part of the Treaty, because of what it said about the League ensuring mutual security and treating an attack on one member as an attack on all, infringed on the sole power of Congress to declare war, so the Republicans opposed it. And thus, in not signing up to the Treaty, the US couldn't join the League.

The UN, by contrast, does not include the principle that other members come to the aid of a member who is attacked so the US felt able to join that. Oddly enough, it then joined NATO, which DOES include this principle. Obviously, having experienced another World War, by this time Congress thought it was a good thing.

For the same reason we should pull out of the UN.

These organizations are the opposite of the intent. Rather than being a way to bring people together, the UN is a sounding board to trash the US and Israel.

Furthermore,they are anti sovereignty bodies.

The U.S., after witnessing the horrors of WW1 wants to return to an isolationist policy.

Many Americans did not want to go to war in the first place feeling it was not really any of our business.

The organizations are a feel good farce. and those in power at the time, knew it.