Do you avoid tax when taking a home equity loan?

You'll be taxed when you sell the house, but not before that (or if you do some other transaction that realizes the gain, talk to your real estate attorney or accountant for more details).

A Home Equity line-of-credit is simply a secured loan: it's a loan, conditioned on if you fail to pay it back, they have a lien on your house (and may be able to force you to sell it to pay the loan back).

Loans are not taxable events. The equity you took out is not income. It's a loan, and you pay it back with interest.

You pay taxes on the capital gain of the home when you sell it. The tax does not take into account any mortgages, HELOCs, or other loans secured by the house. Instead the tax is calculated based on the price you sold it for, minus the price you bought it for, which is known as the capital gain. You can exclude $250k of that gain for a single person, $500k for a married couple. (There are a few other wrikles as well.) That would be true regardless of the loan balance at the time.

(credits to Joe's answer above which alluded to what I was not considering)

You aren't "bypassing" the tax liability if you invest in a home instead of, say, stocks.

It's true stocks would be subject to tax during the year you cash in on them while the proceeds of a home equity loan would not affect your tax liability. HOWEVER, by taking on a new loan, you are liable for repayments. Those repayments would be made using your income from other sources, which IS taxable. So you can't avoid tax liability when financing your child's college education by using an equity line.