Could brushing your teeth too much cause gum disease?

No. No. Gum disease is untreated bacterial infection that produces irritants that cause the gums to swell and cause bone to be lost, which leads to gum recession and loose teeth. Overbrushing can lead to gingival (gum) recession if too much force is used, as in heavy scrubbing motion or using a hard or firm bristle toothbrush.
Not directly, but.. Tooth brushing is absolutely your first line of defense against gum disease. But people who brush their gums "too hard" can actually cause great harm. Being too rough on your gums can lead to recession. When gums recede, the roots of the teeth and surrounding bone are susceptible to further bacterial attack. That- is clinical gum disease. So brush properly and gently and don't forget to floss.