The most common and most likely answer to this crossword clue is the 10 letter word DOGMATISTS
I've seen this crossword clue in The Guardian
D
O
G
M
A
T
I
S
T
S
More clues leading to the result DOGMATISTS
Buddy explains!
The straight part
We know that "assertive types" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case assertive types = dogmatists.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.