No, that's just bad financial management. Spending $48000 to send your kid to a private school is a choice that parents can make when they're wealthy enough to do so.
"Living paycheck to paycheck" means that you just barely make enough to pay for food and rent, and don't have any spare money to cover unplanned costs like medical care. Spending a ton of money on vacation and private school is by definition not living paycheck to paycheck.
No it doesn't. Living paycheck to paycheck means you don't have any left over each paycheck, and the worse version of it is that you don't even have emergency savings left over in case unforseen costs come up.
"Living paycheck to paycheck" means that you just barely make enough to pay for food and rent, and don't have any spare money to cover unplanned costs like medical care. Spending a ton of money on vacation and private school is by definition not living paycheck to paycheck.