Painting - furniture paint application

I am painting an old bedroom suite. I've spray (air spray) Kilz 2 primer on the bare wood and it has looked really nice and smooth after sanding (spray application not the greatest for me as an amateur, but sanding helps). Now I am tryilng to spray Behr semi-gloss Latex on and it's looking bad - very rough and sandy surface and it all just sands right off taking paint surface with it. I've been reading here about BM waterbourne paint and SW Cashmere paint. Help, please. Should I not spray but use a brush? I want the original factory lacquer look as much as possible. Should I use different paint?
Thanks!

o.k. after inquiring with someone else, it seems there is a reason Behr requires an airless sprayer. I am an amateur at this. I don't think I'll be able to get around the rough sandpaper feel to the paint surface since I'm using an airsprayer. So, do I continue with the latex? I don't want to have to redo this furniture in my lifetime. It has been so time consuming. I am looking for a smooth surface.
Thanks so much!

Kilz 2 primer on the bare wood
Not my first choice for bare wood. It doesn't penetrate well, and dries pretty fast = poorly bonded prime coat. But its already there so we'll work around that.
tryilng to spray Behr semi-gloss Latex on and it's looking bad - very rough and sandy surface
Behr semi-gloss doesn't level very well, especially if using a sprayer with the wrong tip or pressure setting.
it all just sands right off taking paint surface with it.
Is it taking the primer too, or just the semi-gloss? If its the primer also, see what I explained above. If its just the semi-gloss, then either there was dust or debris on the primer, or the sprayer might be laying on too thick of a coat. Make sure the sanded surface is thoroughly wiped clean and dust free before applying the next coat. A tack cloth works good for this. I don't understand why Behr s/g would require a sprayer of any kind.
I've been reading here about BM waterbourne paint and SW Cashmere paint.
The Cashmere is mainly for walls. The Waterborne Impervo is the right product for this application. It dries hard and levels beautifully. If you prefer Sherwin williams products, their ProClassic Waterborne enamel is top of the line also.

Once again, I don't know why you would need a sprayer for this. An expert painter might use an airless or HVLP in a spray booth to do this, but that is pretty advanced painting skills. I do furniture often, and you can achieve a nice smooth finish with a brush and roller, with the right product. Roll on the paint to a specific part, then brush it out to even it up and lay it off for the leveling. It can be done.

Hope that helps.

The primer is not coming off. It actually looks quite good to me - very smooth and a nice hard finish. Spraying the Kilz primer did much better than using a brush. It was thick and left brush marks. With spraying the primer, it only took light sanding between coats using a 320 grit. However, spraying my first coat of the color latex semi-gloss, it seems that it was dry before it touched the wood - although I was about 6 inches away spraying. So, the surface ended up gritty to feel and sanding made it all come off in a powder that I could see some of the primer underneath. That's when I read on the can not to use an air sprayer. But, I'm afraid a brush will leave marks and uneven leveling. Hence - help!
So, should I brush with the semi-gloss paint I have? Try an oil? Use floetrol with the existing latex paint? And, if I do end up brushing on the final coat, do I still sand it to smooth it, maybe with a 400 grit?
Thanks so much! I like doing this, but I want to do it right and not have to do this piece of furniture again. I don't mind spending extra money to buy the proper paint to make it right. Thanks!

I don't mind spending extra money to buy the proper paint to make it right.
Get the Sherwin or B.M Waterborne. It will look good with a brush if stroked out well. These paints level beautifully.