"Can’t help but" vs. "can help but"

Solution 1:

I can’t help but think this is a difficult question means that I have no alternative to thinking that this is a difficult question. I can help but think this is a difficult question is not something a native speaker would say. The combination can but is used in sentences such as You can but try, encouraging the person addressed to attempt a task whose outcome is uncertain.

Solution 2:

Can help but Infinitive and can help Gerund are both Negative Polarity Items (NPIs).

That means that they can't occur grammatically outside the scope of some Negative trigger. So they're just fine in a Negative context (here with can't instead of can)

• I can't help thinking he got the better of us in that deal.
• I can't help but remember the smile on his face.

but they're terrible outside a negative environment (what a difference an -n't makes!)

• *I can help thinking he got the better of us in that deal.

• *I can help but remember the smile on his face.

  Summary: If Negation is involved, look for NPIs before doing anything else.

Solution 3:

"Help" here is not used as in to assist.

"I can't help it."

This means I can't stop/control myself, or I have no other choice.

Some examples:

I can't help but laugh at her misfortune.

When the music gets funky, I can't help but dance.

I can't help but wonder if he was just being nice to get something for himself.

I can't help it! It's involuntary.

Solution 4:

This usage comes from a very old meaning of "but" in which it means, literally, "outside". Its original form is the Anglo-Saxon "be outan", which we can gloss as "by out", i.e. "outside". This use is still found in Scots where they might say "He's waiting but the house".

Anyway, there's your etymology lesson. As far as i know, this ancient prepositional "but" is the ancestor of all the many uses of "but" that are in English today, and it has as its not too remote ancestor the "but" of

No one but me heard the remark

which without sounding too weird , we could put equivalently as

No one outside me heard the remark.

It looks to me like a lot of the NPI uses of "but" come from this old prepositional meaning. You use this sort of but to say that nothing "outside" a particular class has interesting property X. "You can't but try" means you have no other option "outside" of trying.