Removing peaceful protesters from any public place, while others remain, is a violation of free speech and assembly.
Think of it this way. You have a house. You have a right to be in any part of your house. Someone forces you to stay in your bedroom. Have your property rights been violated? Your theory says no.
Free speech doesn't give us the right to be heard
No one has to listen to the protesters, including the president. Just ignore them. Forcefully removing them however, is entirely another matter.
Life isn't perfect, is it, not even in a representative Republic, but it is far from unbearable.
My gripe is that I bought and paid for my house, but yet the government sends me a bill for rent every year-if I spend money making improvements, my rent goes up. My car is paid for and yet, the government sends me a bill for the privilige of owning it.And the list goes on.
My country, my President, my family and believe it or not even myself are not perfect. But they are all perfect enough that I would offer my life in defence of them all.