But you made a counteroffer instead, which had two results. One, you terminated that first offer by rejecting it. The counteroffer was that you would eat some of your veggies if Mom let you have dessert. She was smart. And you ate a little bit, a little bit of your veggies.
Offers can also terminate due to lapse of time.
If the offer states that it terminates at a specific date, and should an acceptance not be made by that time, then that offer is terminated. Even if an offer states no time for termination, it automatically terminates at the end of a reasonable time. Of course, reasonable is an extremely slippery concept. The fifth way an offer may be terminated is through intervening illegality. This is when the subject matter of the offer becomes illegal after the offer is made but before it's accepted.