Why do we name people with non Kosher animal names like Dov, Aryeh, Zev etc. But seeing them is avoided?
Because there are a lot of positive elements to those animals. There is a lot we can learn from them. The Mishnah tells us to learn to be bold like a leopard, light like an eagle and strong like a lion. The Gemara tells us that we could learn modesty from the cats, not to steal from the ants etc.
The issue is only seeing the animals because they have negative forces associated with them and that could affect the purity of our eyesight.
Even this is not Halachically forbidden. It is an extra measure of piety, purifying our eyes to the maximum as a preparation for the advanced level of spiritual and G-dly eyesight we will experience when Moshiach comes.