It looks like we happened to run into each other a little too early.
Last night, I met a guy who's looking for no strings attached fun at a club and I know I shouldn't be into him, but he was really my type.
"Are you seeing anyone now, Nicole?" "Yes, I’ve been seeing Eric for a year." "Wow, where did you guys meet?"
You exit your house and you meet someone. You didn’t mean to meet them, but it happened anyway. That’s why this word means to meet by chance.
The reading is that of the word 出る and the word 会う, both of which you've hopefully seen. The 出 portion may be confusing, but you can usually assume that if one part of the word is kun'yomi / vocab reading, the other part is too, which is why 出 uses the vocab reading.
Oh by the way, this word can be written like this too: 出合う. It’s not as common, but you may come across it every now and then, so it’s good to know!