I was married for 32 years and recently got divorced, so dating is a whole new ballgame for me. I recently fell in love with a man who has been married twice and has a LOT of former girlfriends. He is a very outgoing and flirtatious person who people are drawn to. That's the good news. The bad news is that early on in our relationship, I discovered he'd been dating other women or seeking other women out when he told me we were exclusive. We got past that, and he says he loves me.
But...
He gets frequent texts from his ex-wives and several women "friends." Some are ex-girlfriends, some are women he's known for a while, some are women he's recently met. Like I said, people are drawn to him. He says there is nothing wrong with this. I say it's on the edge of cheating.

My question is...am I being overly sensitive to let these texts bother me? It seems to me that if you're in a relationship, you don't carry on continuous text conversations with other people of the opposite sex. Is that too old fashioned? Beside the point of flirtation, it seems really disrespectful to me as his girlfriend. We've discussed this several times, and he knows how much it bothers me, yet insists the women are just friends and he doesn't want to hurt their feelings by not responding. (Never mind that he sometimes initiates a text thread.) Btw--I'm not even sure any of them know he is dating someone seriously.
I do think he loves me, but I'm not sure I can get past this issue. Am I wrong to let this bother me? Does this sound like a healthy relationship?