The most common and most likely answer to this crossword clue is the 12 letter word AILUROPHOBES
A
I
L
U
R
O
P
H
O
B
E
S
Buddy explains!
The straight part
We know that "We wouldn’t like Felix" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case we wouldn’t like felix = ailurophobes.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.
What does AILUROPHOBES mean?
AILUROPHOBES noun- A person with an irrational fear or hatred of felines.