Why was it nearly impossible to create a coalition sizable enough to gain the majority in the weimar republic

There's no real certainty as to what caused it. There's multiple factors but two factors that are important are:
There was too many parties to vote for so no one party ever got enough support, and there were many splinter parties popping up because of it
Also, in an emergency, the president did NOT need the agreement of the Reichstag, but could issue decrees. In the end Hitler took advantage of this shaky situation to take power.
Notably, Weimar has many economical and political issues going on, as well all cultural, but the two I talked about, are probably most notable.