Does the phrase 'the contradiction of healthy obsessions' make sense?

It's an oxymoron :)

Maybe since obsessions is plural, there are two healthy obsessions which seem contradictory.

It was odd seeing Tony disheveled and sweaty. He was out of breath. His trimmed hair fell in loose waves and when he took a drink of water, it trickled down his neck. At work he's so particular and organized. He tends to every detail but at the park he was a regular guy. The contradiction of healthy obsessions actually make him seem more interesting.

Either that or your first instinct is right. An obsession is not typically considered healthy.

the phrase is too sort to make sense its like saying "how to be part" simply doesn't make sense...

Yes it does. I would interpret it the first way.