If you don't want them to be flirty all the time don't give them the romantic trait.
Edit.
When you select to travel somewhere all Sims on the current lot or that you have met are available as possible travel mates. Use the filters if you don't want to see everyone.
And what makes you think either of them have that? Plus I had one literally jump up from his computer and run across the street to some random townie to do the enchanting intro to him. So what does that mean? I have to board them up in their house not allowing them outside at all by removing all the doors? What kind of life is that? I shouldn't have to stop playing the game if the game allows for stupid things like that to happen. For all the reality they put in the game, this kind of behaving is not the reality I want or is normal. Could you imagine sitting on the couch with your significant other and they just bolt out the door to someone they haven't met yet and start flirting with them? How real or logical is that? Just stupid. So yeah, loyalty traits should be a thing.
Do you have any Items that put him in a flirty mode? I have never seen a Sim do flirty stuff without being flirty.
Why did you buy him the reward trait that allows him to make enchanting introductions if you want him to stay faithful?
Do you use Mods?
Nope. I have no mood enhancers enabled in their house plus that sort of nullifies the entire thing if they're out in public. I didn't buy the reward trait. Enchanting is part of the charisma skill. The Sims 4's Charisma Skill is learned every time your Sim engages in conversation with other Sims, no matter the circumstance. So again, what am I supposed to do? Lock them in their house with no doors and forbid them from talking to other people? And no I don't use mods. I have no need for that.
