A lot of the stuff in Europe is just a given whereas in the US, almost nothing is a given. Even the leftists in the US are quite modest with their essential demands in comparison to most of Europe!
Also, compared to the U.S., Europe is decidedly more tribal. There is a sense of national identity forged by foreign occupations and attacks, especially among the smaller or weaker nations, that produces a lot of entrenched, insecure nationalism. Americans, being the top dogs of the world's pack for generations, generally do not understand how nationalism can arise from conditions of humiliation and victimhood, or only limit this understanding to their own black population, thus misunderstanding the European political currents a lot.
If a quarter of your population was forcibly deported to Siberia (which happened in the Baltics recently enough that witnesses are still alive), you will be a lot more jaded and distrustful than if you have no concept of such threats.
Europe isn't "left" leaning at all. Most of Europe is culturally conservative. It's just like unlike the USA, Europeans believe in strong central governments and even the right usually don't question welfare state.
But it says nothing about Europe and wedge issues like homosexuality, immigration, ...
The fact the far right in countries like France for instance have high voting scores should dispel any sense of Europe being "left leaning".
> Many European countries do not have a political party that is even as right leaning as the Democratic Party within the USA.
This is completely false. Every European country has a far right party, that holds "traditional" view on wedge issues and is opposed to the US made idea of "diversity".
I don't know why americans think Europe is somehow "left leaning", this has never been the case. The divide is more along the lines of "globalists" which are classical liberals and pro EU, and nationalists/isolationists, which are anti-EU, anti-globalism. Both camps have their socially liberal and culturally conservative parties.