It us incomprehensible to me what kind of problem a doorman could be giving you that you avoid him. If it is so bad complain to who is running the show. Are you a unit owner or a renter?

WHAT?????? Sexist? Do ya THINK??? 
 
Have you told them you have had an issue with one particular doorman (employee your condo fees -assumption-pay for),and that you are intimidated enough to feel you must enter through another door? Do other residents (male and female) have a key to this door?  
 
What if you were a male? Could he have issues with a vindictive girlfriend, or if you had a husband you could have a troublsome divorce from? Good grief what century do they live in??? Demand a key and don't take no for an answer. If that fails, inform them that they have violated your civil rights and the rights of an owner to obtain entrance to all facilities and points of entry/exit. 
 

Someone sent out an anonymous letter which stated that he receives full benefits and a $100,000. life insurance policy, he thought I wrote the letter (I didn't) and he cursed and yelled at me. I am an owner, but the board and the residents here all think this guy is the greatest. I don't receive any backup regarding this doorman, so I avoid him.

Well try convincing him you did not send a letter and man up. Carry a recorder with you and go through the door. If he misbehaves, you have recordings the board cannot ignore.

Sounds like a terrible situation! The board needs a better reason than that to say no regarding the key -- if it's an entrance that no other owner has access to, it's a different matter, but if other people have access, they need to allow you access or give you a valid reason why they can't. That they would even say that to you regarding a boyfriend is ludicrous -- I hope you have that on paper! 
 
As another poster said, don't take no for an answer. You are an owner with rights.  
 
As for the doorman himself, if you feel threatened, I would tell the board that in an official letter. They have a legal obligation to follow up on your concerns. If something (heaven forbid) were ever to happen, they would be liable. You pay too much to live in a condo and feel uncomfortable by someone who lives or simply works there.  
 
Good luck!

Go through the front door with dignity. Carry if possible a recording cell phone. If the door man harrasses you, glares at you ,  
 
speaks disrespectfully, keep a record of every bad encounter. 
 
Start by sending a certified letter to the board with your initial complaints about the door man and your speculation about why he is harrassing you.  
 
Get everything on paper. And via certified mail. This might get their attention and their anntenna up about possible legal action. I would also think about making a report to the police for disturbing of your peace and harrassment.

You have received a lot of comments to consider. This man sounds paranoid. Do not have any conversion beyond business. If he continues to try to falsely accuse you,say bluntly that his problem has nothing to with you and walk away. Make no eye contact. Mean business, that you are not going to be messed with. Report every accusation to your board with a certified letter. By the way if the letter is true, owners have the right to know what the association pays its employees, and to take any issue with it that they please. The doorman is out of line. If the letter was sent to owners and true that is the owners business not his.