We answer income tax question in this user forum. You have a legal issue. Seek advice from an attorney,
GET A LAWYER!
Even if you owed taxes (not much) would you rather pay a small amount of tax, or never get any money.
You bought a house together, you want him to "buy you out" of your half. You need your name off the title, off the mortgage, and you want your money. If you sign a quit-claim deed to take your name off the title, without a check in hand, you won't have any leverage to force him to pay you. You can get a real estate lawyer to protect you for $500-$750, which is less than 10% of your hoped-for profit. Well worth it.
For taxes, you will owe capital gains tax but only on your gain. Here's an example of how that works:
Suppose you bought the house for $100,000, you each put down $10,000 and had an $80,000 mortgage, and you are 50/50 owners. Your "cost basis" in the house is $50,000.
The house is worth $120,000 today. You will sell him your share for $60,000. After paying off the old mortgage, he owes you $20,000, which is your share of the downpayment plus your share of the "gain" in value from the original purchase.
Since your cost for your share was $50,000 and your proceeds for your share were $60,000, you have a $10,000 capital gain. You don't pay any tax on that capital gain as long as you lived in the house as your main home for at least 2 years, and you moved out less than 3 years ago. If it was not your main residence, then capital gains tax is 15% for most people, as long as you owned the house more than 1 year. 15% of the gain would be $1500, plus another $500 for the lawyer, means you net $18,000. Instead of getting whatever he feels like he can get away with after he owns the home free and clear.