Why does left recursion have to be eliminated?
I am assuming that you are talking about context free grammars.

There is no difference between the two grammars. They are a different representation of the same set. 

What do you mean by a problem?

Left recursion is a problem for LL(k) parsers, but they can handle right recursion. LL(k) parsers are preferred because of they use less stack space and they tend to be faster (not always though).