I hate traveling by airplane.

Literal

Airplane [by-で] travel [nominalizer-の] [topic-は] dislike.

で marks the means of transportation. ~のは...嫌い uses the nominalizer の to turn the verb phrase into a topic, then comments that the speaker dislikes it. 嫌い is a na-adjective meaning 'disliked,' not a verb — a key distinction for learners.