Road Rage On The Bike Path

So commuting by bike is supposed to be my healthy alternative to the madness that is commuting by car in Houston, but tonight I got in a bit of a row on my commute home.  This happened where the shared use path around Barker Reservoir ends at Sergeant Hatch Park.   You know where people who drive their cars, to go ride their bikes, end up parking.  So I am coming upon the exit of the path and there is another rider approaching from the other side to enter the path.  There is only room for one bicyclist at a time to pass.  So who has right of way when two cyclists are approaching at nearly the same time?

My first rule is if there is a brutal wind whoever is eating the 20-30 mph headwinds has my respect and the right of way.  Barring that I think it should be the person exiting.  Here is my reasoning:

1) Do you barge onto the elevator when the doors open and before people have a chance to get off?
2) In this case I was in the middle of my ride/commute and the other rider hadn't even started his ride, he can wait.
3) I'm riding with fully loaded panniers on each side of the bike.  Cut a guy some slack.
4) But mostly his ride hadn't even started.  Let the other rider exit the path and then go!

So as I approach the exit the other rider makes no assertive move or clear intention that he thinks he has the right of way.  He was kind of paused before the gate and I decided he was waiting for me and I made my move.  As I passed through the gate we came close to each other and he looked uncomfortable, I almost think he was having trouble getting in and out of his clips, and loudly called me an "idiot".  I didn't take to this at all.  I stopped my bike dropped a "F You" back to him, invited him to stop, turned my bike around and went through the gate, re-invited him to stop, and called him a spiteful woman with a 5 letter word but he kept riding away. Of course I am going to keep my eyes out for Mr new bike, new kit, can't get in his clips, drive to go ride his bike, shit talker.  I got a couple ideas for him.

Then a couple miles into George Bush Park I saw a young girl getting helped to the trail parking area.  It looked like someone was calling her an ambulance.  From the way they were immobilizing her arm at the elbow I think she had a broken collarbone.  Just a nasty injury.  I feel terrible for her.  I want people out on the shared use paths enjoying their bikes.  I guess in retrospect I'm glad the "idiot" caller didn't take me up on my offer.  We should be having fun out there folks!