Why are rising sea levels a problems?

They are a problem because it could cause flash flooding in one place while causing a drought somewhere else.

Most of all, there are a lot of cities on the coast: for example LA, NY, Lisbon, Sydney, Barcelona, Rio de Janeiro. Those cities have a big population. If the sea level rises, people will have to move away from those cities (and if it rises rapidly, they might die in the flood).

Further, it could contaminate our storages of drinking water (sea water is salty and can't be drunk).

Also, it will mean less land, which also means less land for agriculture.