Well first, I was young. The first President I remember was Ronald Reagan and he was a Republican. I also had a lot of respect and admiration for George H.W. Bush (still do). So this inclined me to be a Republican. On top of that, I was raised within the conservative evangelical religious context and thus my early thinking was shaped by this. I was pro-life, against gay marriage, etc. I also bought into the domestic policy arguments that Republican politicians made and didn't really give them much serious examination until later.
Well, there is a lot that turned me towards the Democrats and progressivism. But I can't quote every source or argument that made me "see the light." There were many, over time.
Generally speaking, I would say the turn began under Obama. When Obama ran in 2008, I supported McCain. I was surrounded by people who literally thought Obama was the devil and the coming anti-Christ. I accepted a lot of the hate that the right propagated against Obama in 2008 without much deep examination of what was being said, etc. However, once Obama became President, I watched him. And I was impressed. I didn't see all the crazy stuff that those on the right saw. I was really impressed with Obama.
It was during this time too that I began to seriously consider my positions on domestic issues. I studied the positions and looked at different sides. I read different sources, etc. I flirted with libertarianism for a bit (I liked Ron Paul in 2012). Eventually though, by late in Obama's term, I had become a moderate on most domestic issues. But I was still socially conservative, which kept me in the Republican Party. Those views however began to change as I gave consideration to the opposing viewpoints. For example, I actually start conversing (and listening) to pro-choice individuals. I also developed a more diverse set of friends which opened me to other viewpoints. Other personal experiences (as well as some changes in my religious beliefs) led me to move further away from social conservatism as well.
The final straw that made me leave the Republican Party was the nomination of Trump and the dark/hateful mentality that overtook the Republican Party, something that had been growing under Obama and came to full completion in 2016. I could not be part of a political party that could embrace a leader like Trump and what he represented. While I was at best a moderate Republican by this point, the Republican Party changed into something I could not be a part of. The day after he was nominated, I became a Democrat.
Since then, as I have continued to study and consider other viewpoints, I have become more and more progressive in my thinking.