Modern Girls & Old Fashion Men
The Strokes Lyrics

You were
Addressing someone, likely a modern girl

Modern girls always have to go (Right on time)
Modern girls are expected to be punctual and efficient in their activities

Old-fashioned men always want a mistress (You were right)
Traditional men often seek extramarital affairs and the person being spoken to is aware of this fact

Modern girls always get their way (I was wrong)
Modern girls tend to be quite assertive and persistent and the artist acknowledges this after initially thinking otherwise

Modern men dream of what they can't say (That's alright)
Men in contemporary society often have desires they feel uncomfortable expressing openly but that's perfectly normal

Right? Right? Right? Right? Right?
Asking a rhetorical question for emphasis

I don't belong (I don't belong)
The singer feels out of place in some aspect

Why you gotta say it if you know it's something wrong? (Why're you sitting over there?)
Asking why someone would verbalize something they know is inappropriate without providing any additional context

Says that he'll apologize and it won't take too long
Someone has promised to apologize soon

Well, you don't wanna trust nobody else (Always thinking 'bout yourself)
The listener is untrusting and only thinks about themselves

(Time)
Announcing a change of subject

There's a few things that are gonna have to change (I'm your son)
Stating that things will have to be done differently and informing the listener of the relationship between the artist and listener

Everyone has the same opinion (Won't you please?)
Everyone shares the same viewpoint and the singer is appealing to the listener to understand

Your time is almost over (Don't be mean)
Implying that the person being spoken to is getting old and asking them not to act hostile

We won't get the chance to do this over (That's alright)
The opportunity for a second chance is unlikely but the singer seems content with the situation

Right? Right? Right? Right? Right?
Asking a rhetorical question for emphasis

I don't belong (I don't belong)
The artist feels out of place in some aspect

I don't want the imprint of your key upon my nose (Why're you sitting over there?)
The singer doesn't wish to have the key to the listener's house on their face and is inquiring as to why the listener is keeping some distance

You don't have to tell no one 'cause no one wants to know
The person being spoken to doesn't have to inform anyone about something, since no one is interested

That you don't have no happiness at all (Always thinking 'bout yourself)
The listener is unhappy and is focused on themselves

Oh yes, we're falling down
Repeating a phrase in a song

So fucking help me up
Asking for assistance

Always thinking 'bout yourself (You don't love me)
Continuing to highlight the listener's self-centered behavior and criticizing their lack of love for the singer

Always thinking 'bout yourself (I am an animal)
Reiterating that the listener doesn't consider the artist's feelings and comparing themselves to an animal

Always thinking 'bout yourself (I am not practical)
The listener's self-focus causes issues and the singer is claiming they aren't being practical

Was I?
Questioning if the singer has been overly critical throughout the song