Why can't a compiler have a "shift/shift" conflict?

Shift/reduce conflicts occur when the parser can't tell whether to shift (push the next input token atop the parsing stack) or reduce (pop a series of terminals and nonterminals from the parsing stack). A reduce/reduce conflict is when the parser knows to reduce, but can't tell which reduction to perform.

If you were to have a shift/shift conflict, the parser would know that it needed to push the next token onto its parsing stack, but wouldn't know how to do it. Since there is only one way to push the token onto the parsing stack, there generally cannot be any conflicts of this form.

That said, it's theoretically possible for a shift/shift conflict to exist if you had a strange setup in which there were two or more transitions leading out of a given parsing state that were labeled with the same terminal symbol. The conflict in that case would be whether to shift and go to one state or shift and go to another. This could happen if you tried to compress an automaton into fewer states and did so incorrectly, or if you were trying to build a nondeterministic parsing automaton. In practice, this would never happen.

Hope this helps!