You're right, it's not actually that fast when you compare it to what it was like millions of years ago, but I agree the pace has definitely picked up a lot. The main problem is global warming. When the temperature rises, ocean water expands - it's like when you heat water from the tap and it takes up more space. Plus, the ice from the polar ice caps and glaciers is melting and falling into the ocean, actually adding more water. These two processes together account for most of the rise we're seeing right now.
The thing is, this is happening way faster than in the past because CO2 concentration in the atmosphere skyrocketed over the last 150 years or so, mainly because of fossil fuels. The ocean could handle slow changes, but when everything changes this fast, coastal cities find themselves in trouble. In Rio it's particularly annoying because you've got the entire South Zone vulnerable, plus areas like Barra that already suffer from frequent flooding. Walls and containment structures are more of a band-aid than an actual solution - ideally you'd stop the warming, but then you get into discussions that go beyond pure science.