I have watched a mad cow chase Bella (she was smiling, Bella not the cow) and so far I have avoided mad cow disease, but this is about neither of those things. MAD Cow stands for Maple-Ash-Dogwood and Catalpa, the native trees around here that have opposite leaves.
Most deciduous (hardwood) trees have alternate leaf arrangement so it is nice to have an easy way to remember those that are opposite. This red maple twig nicely shows the paired bud and twig arrangement.
This white ash twig does not show buds this time of year, but you can see the paired leaf scars (sites of last year's leaves).
The beech is already showing its bronze, cigar-shaped buds alternating on a zig-zag twig.
Of course there are always exceptions, such as the alternate-leaved dogwood! And many shrubs have opposite leaf arrangement. I will save that for another day. In the meantime, think about Bella being chased by a mad cow and you'll remember the opposites: maple-ash-dogwood and the catalpa.