It's not unattractive just to want to be in a relationship. That's silly. Usually, when people seem desperate or creepy, they're doing at least one of these other things too:

• Treating potential partners as objects of desire, or targets, instead of as people

• Being more focused on the endgame than on actually enjoying the conversation or getting to know the "target" in the moment

• Proceeding through a set of pre-rehearsed scripts instead of actually being mentally present and participating in the conversation

• Becoming anxious about whether or not things are going the way you want them to, and allowing that anxiety to negatively affect your participation in the conversation

Basically, these actions communicate, "I care about acquiring a SO, but I'm not actually terribly interested in you or this conversation unless you're going to further my goal". It's awkward and unflattering for someone to be visibly uncomfortable and unhappy while conversing with you. It's insulting for someone to make it clear that they see you as a means to an end.

But probably most importantly, it just isn't any fun when someone is having this type of interaction with you. Nobody is going to be interested in you if you're not making yourself enjoyable to be around. And even if it's not offensive/awkward at first, asking for a number or a date after ten minutes of unenjoyable interaction is insulting - when someone clearly hasn't noticed that you were completely not into it, and tries their luck anyway, then it immediately becomes clear they really don't care about how you feel or how compatible you are with them - they're just trying to, again, use you as a means to an end.