The definition of coincidence :

1. A remarkable concurrence of events or circumstances without apparent casual connection.

2. Correspondence in nature or in time of occurence.

Synonyms: accident, chance, concurrence

The definition of fate:

1. Noun- The development of events outside a person's control, regarded as determined by a supernatural power.

2. Verb- Be destined to happen, turn out, or act in a particular way.

These two word are very different, but are used by different people often times to describe the same event. 

All you know is you don't believe in fate.  Or you didn't.  But then again, neither did you believe in chance.  Was there some in between state?  Some way to descibe what happened?  You didn't think so.  Because if there was no in between, then you can't just not believe in one.  And that also means that there is no word to describe what happened that day.  You didn't really even know what happened.  It just was.  You didn't personally will it to happen, and neither did he, yet it wasn't an accident.  It was from some purpose that you two met...