How do you explain to others your change in your faith?

Absolutely agree. 

Something non-Catholics often don't realize about the church is that it has a prescribed lectionary of readings for each Sunday. Over the course of a three- or four-year cycle (I forget which), Catholics hear most of the bible read and/or preached on at mass. People who attend mass each week tend to know the bible very well. Contrast that with other churches where the pastor and/or bible study leader decides which passages he thinks are important and may cherry-pick to suit his views.

When I started to question what I had been taught, the first thing I did was to dive deeper into Catholic apologetics, looking for arguments to shore up the beliefs I'd been raised with. That took me to counter-arguments from protestant and evangelical theologians. The more I read, the more I became convinced that all of it was made up to suit the wishes of those who wanted control - of the poor, of women, of anyone less powerful. Catholic tradition, upon which a fair amount of their canon is based, is most definitely non-scriptural. But the scripture-only churches lie when they say they don't rely on tradition or other non-biblical beliefs. Deciding which scripture to follow and which to discard, deciding how to interpret certain passages in translation, even deciding which translation to use - all of these are forms of tradition that have been created to benefit those in power. 

As you've said, though, you can't convince somebody who hasn't seen it and doesn't want to. Many will actually be offended that you've read the bible and significant amounts of theology and still don't believe. They'll tell you that you just decided not to have faith because you "wanted to sin" or were "tempted by the devil." I had someone actually tell me the first one on this board years ago, now that I think about it. My question always is, as a faithfully married mother of two who lives a pretty boring life, what is it that you think I'm doing for sins that I had to leave the church to do?

That's why it's better just not to share. Many believers are offended if you have been exposed to/immersed in their belief system and still don't accept it. 

(And yes, biblical references abound in our culture and literature. I sometimes have to explain them to my kids.)

I don't!

You could try saying it's something deeply personal, I'm working through it, and I'll discuss when I'm ready. 

Otherwise, I know I'd get ugly and shut it DOWN.

I have changed from a rather conservative Christian in my 20s to now a very liberal follower-of-Jesus who's okay not really knowing for sure in my 40s. I haven't really had to explain it in words so much as just lived it & people can see how I have changed, KWIM? I volunteer with Moms Demand Action and Free Mom Hugs (which is specifically a pro-LGBTQ organization) as well as attend a church that uses "She" and "They" pronouns for God in our songs & prayers. I also attend reproductive rights rallies and was the impetus for the "anti-reunion" my high school class held at the same time as the official reunion in protest of an alum who is notorious for his sexist/racist/homophobic platform as a local pastor and fledgling author and was on the planning committee. I share all these things on social media and bring them up in natural conversation with friends, family, etc. so everyone knows.

The older I've gotten, the more I've realized that I don't really know much at all. Does God exist? I don't know. Is there a Heaven? I don't know. Am I doing the right thing? I don't know. I figure that loving God and loving my neighbor is good enough, and we'll see how the rest shakes out. I have several friends + my husband who lean towards atheist/agnostic, and we choose not to discuss it at-length; we accept whatever the other person is or isn't and enjoy our time together.