Question

Will charging your phone halfway and then pulling it out damage your phone?

Answer 1

I don't think pulling it out halfway would damage your phone itself nor the battery. Your battery life depends on a lot of different factors though. If it's a lithium ion, like most are, then keeping it topped off is best, also don't store it in very hot conditions, e.g. leaving it in your car on a hot day.

Further information about this with Lithium Ion cells can be located here.

Answer 2

No it not because pulling out your phone out of the charger does absolutely nothing to your phone you should worry when the phone is at full charge and then you still don't pull it out the phone will overheat.