The alternative is working with your employees to get them the time off they need to the best of your ability instead of hiding behind “the needs of the business”. They don’t give a flying fuck about the needs of your business, especially if you don’t give a fuck about them enough to approve a day off request.
Any time I’ve EVER had trouble accommodating a time off request, I’ve done it in person and it started with me trying to figure out what their time is for so I can work with them on finding a way to accommodate their plans. Or, if it is clear that person 1 must be off, then I can talk to person 2 or 3 with requests and work out a deal with them instead.
Instead of any of this, sounds like this terrible manager simply denied the request in the schedule with no conversation and KNOWS he’s a dick, given the “keep frontin’” comment.