Because it's typical for a new cyclist to huff and puff and feel stressed during a perceived hard interval, he never takes his HR to it's max. As a general rule, it takes a lab or a seriously competitive situation to see your max HR. Join the fastest group in your area and ride with them. Do everything you can to keep up, and you will likely see your max HR. It's usually accompanied with sick feeling in the stomach. If there are no fast groups, then go to a lab. Its only about $200 and they will find your max HR, as well as your lactate threshold and power threshold.

Increasing HR with age might be a sign of cardiac drift. Not a big deal, as it affects lots of people. I have it. I can ride at 175 HR at a constant effort, and after a while it starts creeping up...until it hits about 191. Problem is the efficiency drops with increasing HR since stroke volume drops. There is a grain of thought out there that people chronic cardiac drift a lot might want to consider a beta blocker. Its contrary to all you read and hear with regards to performance but, if it mitigates the drift then your stroke volume is better and thus performance. i guess it's a tradeoff.