I feel that when he makes the claim of "never" is where you are having a problem. You really should try to figure things out on your own because that is the only way to are going to permanently attach the solution to the problem. When others help you, the solution doesn't always stick and you are left coming back when you run into something similar months down the line.
Now if you are banging your head into the desk for multiple hours, then maybe you should have asked for help. But as he points out, there are situations where (as a tech lead for a startup) you aren't going to be able to ask for help.
You are taking what he says as "I'm so smart I don't need help" instead of seeing it as "I may not know how to fix this now, but I am determined to figure out a way". You are attaching a very negative view instead of seeing it as resilience in the face of a problem.