A is better than B and C.
This sentence is ambiguous.
It can mean one of two things:
- A is better than B, and A is better than C.
- A is better than the combination of both B and C.
Using than twice is one way of making the first meaning explicit.
The other way is this:
A is better than B or C.
So, your colleague is wrong in that you shouldn't just remove the second than if you want a sentence whose meaning is explicit. If you remove the second than, you need to also change and to or.
Update: As has been pointed out in a comment, if we equate natural language with symbolic logic (which is not always how English works—because English is neither completely logical nor mathematical), then the following issue could arise:
- A is better than B.
- A is not better than C.
But this statement would still be true:
A is better than B or C.
It would be true because A is better than one of B or C.
If we allow for that additional interpretation, then one of the following could be said:
A is better than both B or C.
A is better than all of B or C.
Both of those are phrased in a slightly odd way—the latter would normally be used only if there were three or more items—but they mean the same thing as the first sense at the start of my answer.
However, in short, keeping the second than may be the simplest phrasing.