As he was speaking, I respectfully cut him short

What you did was not respectful, it was rude and hubristic.

What it entails is that we respect whoever it is that we come across regardless of age difference or position

Wrong. Respect is earned, not a right. And besides, you did not respect that other person at all, you selfishly cut him off.

That man failed to understand that,

Maybe you failed to understand that the elderly man simply wanted some company, someone to talk to as he is lonely. Maybe you should have made more of an attempt to be personable and patient and to hear him out rather than put your needs above his. You're selfish.

they also feel the need to speak to them as they please

And yet you spoke to him as you please without any thought to his feelings or motivation...you didn't even have the courtesy to let him finish speaking. You're ill-mannered.

I feel that we do not need to seek respect to get it

So you want people to respect you without even doing anything to deserve it? Of course a person needs to seek respect and they do that in many ways including how they treat others around them.

no one deserves to be spoken to in a manner that is degrading or undeserving

And yet, you brutally cut of a person as he was speaking which he probably didn't deserve.

they must not be in the attitude of disrespecting others

But it's ok for you to disrespect others.

You look like you're about 11 years old...maybe you should go and learn about life before you start dictating about it to others, and while you're there, learn some manners as well. I feel like you have none.