"In addition to one carry-on item, you may bring one personal item such as a shoulder bag, backpack, laptop bag or an item of similar size"
All of those items and items of similar size would easily fit under the seat in front of you. So if your bag didn't, then you were indeed not following the rules, and she had every right to check your bag.
"Any item in excess of carry-on baggage size or allowance requirements as listed above will be checked to your final destination and may be subject to applicable checked baggage fees"
Putting your second personal item under the seat in front of you is also common courtesy, so that as many people as possible can get there carry-ons stowed before the bins get full.
She didn't have to be rude, that's for sure. But I can't really say I blame her.