Fat Burners For You

Today a trainer at the gym told me that I have to strength train before doing my cardio. He said if I reversed it, I’d be destroying my muscles. Other trainers have never told me that it’s bad to do cardio then strength training and I read somewhere that if you want to improve your cardio health and lose weight that you should cardio then strength train and if you want to build muscle you should flip that routine. I want to lose some fat (I’m 5′8″ and 140 lbs), strengthen my muscles (core in particular), and just be healthier overall. When I’ve worked out in the past, I’ve ended up lowering my body fat percentage and gaining weight because I was building muscle. Does what this trainer said make any sense? Have I been doing it all wrong?