But or But Not?

"I brought my luggage but not my passport." Is the equivalent sentence.

"I brought my luggage but my passport." is not a complete sentence, we are left wondering what is different about the passport. A complete sentence might be "I brought my luggage but my passport is still in the hotel safe".

'But' is a conjunction and when we use it there must be two statements, a statement of an initial condition and a statement of a contrasting one. For example "I can't come tomorrow, but I could come on Monday". In "I brought my luggage but my passport" the phrase "my passport" is just a noun phrase and does not form a contrasting statement.

"But" is sometimes used at the start of a sentence to introduce an objection to something someone else has just said or something you have written in the previous sentence, often to explain why an instruction or suggestion cannot be carried out. For instance Alice might say "We can go and see Bob and Carol while we're here" and Dave might say "But they're in France this week".

It used to be taught that sentences should never start with conjunctions, but that is not taught now. But (do you see what I did there) there must still be statements on both sides of the conjunction that are related in some way.

If you started a speech or an entire piece of writing with 'But' your readers would wonder what you were contrasting the next statement with. The only way in which you could do that would be by starting with quoted speech for some reason. For instance a motivational speaker might begin a presentation "But I can't do that" you say. I tell you you can! Think positively and you can achieve wonderful things.