Search Results: he is still on the dating site

I can think of one example in my life and one example in a friend's life where a guy was interested in her and also another time where a guy was interested in me, when I resisted they pursued but when I pursued, they resisted. I did not date the guy cause he was turned off by the fact I initiated contact but when I avoided him he would sacrifice other events to chase after me, but this was years and years ago.

My cousin says the same thing to her friends that if you want a guy to like you, you should ignore him. I don't know if she still gives advice cause she is at the age where a lot of her friends have settled down and are no longer on dating sites.

Here’s the gist. I’ve been dating someone for about 2 months, things have been alright but the other night we said I love you to each other, I initiated that but wasn’t expecting a reply of the same.
I have feelings for this person clearly but want to make sure that there’s nothing I should be worried about. So I did some digging (I’ve been hurt too many times in the past to not first dig around and see what’s up.).
First thing I find is their dating profile on the site we met is still active. Ok…not promising…
But then I found a profile of them and another person together like a joint profile explaining they were looking to hook up with a third and to contact them if interested.
The other thing I’ve noticed is, my significant other never asks me about my personal life or family, everything is surface. I’ve also noticed they do what I call parroting our conversations. So if I say something they say almost the identical thing back to me or will just ask me the same question I just asked them while trying to get to know them.
Break up or stay. What should I do?