It depends on the person. Some people are overcontrolling like that and they want to cut you off from all your friends, and have you only talk with theirs and hang with theirs... if you do not want to do this. Then you tell them No, and if you want to introduce some of your friends to him or her that they are worrying about this may help relieve the anxieties of.. maybe so and so is trying to him or her away from me...

Never, allow you significant other to control your social life if you do not want to this includes internet.. However.. Not always is the person asking necessarily a control freak.. They may not realise these social networks are just not just for finding dates.. as many are geared towards just that.. or they may have social anxieties... in general and get nervous about anyone who is not in their little inner circle of friends..

I have an ex who was like that.... Major social anxieties and for years I tried to work with them, and I just no longer could handle being in a relationship where I was treated like I can not be trusted.. But.. Others can handle that type of relationship.. and if they can more power to them...

I tend to be bad with dating relationships in general so I slipped myself back into the undatable catagory for now. :) .

You also have to ask.. Why is this person worrying? ...
And ask them what you could do other than not deleting your accounts what you can do to ease their worry.. encourage them to make an account and add you.. then when you or him are away you can socialize with eachother and introduce eachothers friends to eachother...

Also look if you are spending to much time on these networks,, and if he or she feels like there is not enough time being spent with them? .. that maybe the reason too..