[susan53]

His jacket, not his shirt or socks, always seems to match his slacks.

This is asyndetic co-ordination - ie co-ordination with the co-ordinating conjunction omitted - but it's odd, as I'll explain below.

The underlying sentence here consists of two clauses co-ordinated by but :
His jacket always seems to match his slacks but his shirt and socks don't seem to match his jacket

The underlined section is the predicate of the second clause.

Not can act as a pro-form for the predicate - ie replace it. This gives us :

His jacket always seems to match his slacks but not his shirt or socks.

(This for me is a much more likely sentence, at least in writing, because of the tension which exists between the subjects of the two clauses and the singular verb in your version. However, in your version....)

The conjunction but is then elided (omitted from the sentence because understandable from the context) leaving :

His jacket always seems to match his slacks, not his shirt or socks.

Here are some other examples of ordinary vs asyndetic co-ordination :

Slowly and stealthily, he crept towards his victim.
Slowly, stealthily, he crept towards his victim.

You can have tea, or coffee or whatever you want.
You can have tea, coffee, whatever you want.

He was thinking of going to Venice first and then Rome. In the end he decided to go to Venice, but not to Rome.
He was thinking of going to Venice first and then Rome. In the end he decided just to go to Venice, not to Rome.

Interestingly with this last sentence I feel I need to insert "just" if I want to use asyndetic co-ordination to emphasise the choice between alternatives. Otherwise to me, it becomes a contradiction :

A : He decided to go to Rome, didn't he?
B : Rome? No, he never even considered it. He decided to go to Venice, not Rome.

which is quite different - if there's a co-ordinator involved it's "and" rather than "but".

This is what's odd about your example. To clarify the fact that it is a co-ordinated clause and not a contradiction, I'd want to include the co-ordinator :

His jacket always seems to match his slacks but not his shirt or socks.

Otherwise I'd understand something like :

A : I love the way his shirt and socks always match his slacks.
B : What? It's his jacket, which always matches his slacks, (and) not his shirt and socks.


Hope that helps.