Some insecurity is normal in a relationship; making problems because of it isn’t.
No matter what we might like to tell ourselves, most of us are capable of being a little jealous when it comes to those we are dating. It’s not nice to think that the special attention we thought was reserved for us might be shared with other people as well; sometimes it pays to be attentive to the small things, as it may add up to a bigger problem later on.
At the same time, it isn’t worth making yourself upset over something that you are never going to have complete control over. Also, there is a fine line between having reasonable worries and demanding that your partner restrict and change their behaviors in ways that are hallmarks of an unhealthy relationship. If you can’t trust the person you are with to go out into the world and interact in a way that respects both their autonomy and your connection to them, why would you persist with the relationship at all?
It’s common for couples to argue about appropriate behavior towards other people, but that doesn’t mean that it is always right to have an argument in the first place. Basic courtesy and friendliness towards the gender your partner is attracted to does not immediately equal a desire to cheat.