Weight training is catabolic too, just as much as cardio.
HOWEVER, the body's adaptive response to weight training creates a stronger anabolic response than the transient catabolic effect that weight training has. That's why the net effect of weights is muscle growth not breakdown.
Cardio you have to look at a little different....unless you are inactive and don't exercise, LISS, and MISS won't be enough of a tension stimulus to cause an adaptive anabolic response (however, in couch potatoes they actually gain a little bit of muscle from LISS/MISS because their baseline of adaptation is so low). However, high intensity cardio that requires large amounts of muscle action can actually cause enough of an anabolic response to mitigate any catabolic effects of the cardio.
Think about how much force a sprinter's hamstring is putting out when he's doing an all out sprint. It's A LOT and very comparable to weight lifting.
So that's the adaptive side of things....however nutrition also plays an effect.
If you go into exercise with fuel; carbs and protein being most effective, it reduces the acute catabolic effects of the cardio and speeds recovery. So essentially it lessens how catabolic cardio is.
Most people think "wait this is bad, I don't want cardio to be working off of what I've eaten, I want it to work off of my bodyfat!"
Well, that's not correct. If you are counting your macros, and eating a set number of calories, who cares if you eat a big meal before doing cardio. A 400kcal session burns 400kcals no matter what, even if you ate 500kcals right beforehand...If you didn't burn the fat exactly during cardio, and instead burned off the food you ate, who cares? You will burn it later when you have 500 calories less in your daily allotment.
In fact, doing cardio without fuel will make it harder to get your Hear rate up and to get solid muscle action to burn those 400kcals, and you will have to put out greater energy to do so, so more effort=more catabolism, and less fuel=more catabolism. That's why IN GENERAL I'm not a fan or fasted cardio. Although it has its time and place in specific instances.
Other things to consider is that even though the adaptive response to MISS/LISS is low, and likely won't have an impact on muscle tissue, if a VERY large amount is done, that can tell the body that you want more oxidative (ie, smaller) muscle tissue since you are more interested in cardio training than weights. So there is a ceiling to how much you can do before it bites you in teh behind.
Also, HIIT, although anti catabolic in its adaptive effects on the body, carries a hefty recovery component, and if your legs are trashed so much that you can't get in a good leg workout, you'll lose muscle....not because of the HIIT, but because you can't lift heavy on leg day.
Controlled Labs Athlete
Drug Free Bodybuilder and Raw Powerlifter
NASM Certified Personal Trainer & Performance Enhancement Specialist