Conversion of FA to Regular Expression
The regular expression is supposed to match (exactly) all of the words that the automaton accepts. If you pretend that some of the transitions of the automaton don't exist, you're effectively converting a different automaton, and that automaton probably accepts different strings from the ones you're supposed to accept.

In this specific case, pretending that there's no $\varepsilon$-transition from the first state to the third one means that the automaton no longer accepts the word&nbsp;$c$.