Someone who really loves you can handle you having your own plans.

A plan of your own is the smallest available test of whether somebody is comfortable with you being a separate person. Real affection can hear that you are busy on Saturday without treating it as ground lost. When a plan reliably causes a problem, the plan is not the issue, and rearranging your week will not fix it, because what is being asked for is not time.

Watch what happens next time instead of arguing about it. Say the plan plainly, with no apology and no trade offered. Relief or interest is one answer, and a negotiation is another.