But yes, in general its yours or someone you know's cash.Yes in the example: 50k house, you buy it with 50k cash, it appraises for 80k, you get 50k cash back out, have a rental that cashflows every month AND have 30k in equity, rinse and repeat

Its conceivable that nothing changed with your tenants, the income stream, or expenses, just one of the 10 members buys out another member for her $50,000 in equity because she is going through a divorce, or some other similar situation. 

Each year I hold  I gain about 7K in equity and it goes up each year after that (8k, 9k, 10k etc).

In exchange, he is willing to give me 200K in equity and promises to continue to pay PITI.

In other words you paid $35k for $85k in equity...if you don't have any loans on it.Subtract the seller financing from it, and your equity goes down. 

However I want to reach financial independence as soon as possible and I don't want to be throwing away my money on rent which is $1k/mo with no gain in equity.

I cashed out 50 some thousand in a 401k and put in real estate.Even after taking the 40% hit in taxes/penalties, if you buy with leverage, you can easily turn that into 130k to 150k in equity in 3 or so homes and net income of roughly 500/mo or so (which is tax free for almost a decade when you factor in depreciation).And its going to grow about the same as a 401k too. 3 houses worth 150k apiece that you're all in at 100k or 110k.

Why would I want $1 million in equity in a building I own when I can use that cash to increase my revenue?

Based upon an appraisal of $50,000 and subtracting the principal I owe the bank of $27,500, this leaves $22,500 in equity.

Most people on this forum will tell you to avoid the 401K because it definitely sucks up capital that could be used for REI.That said, for the average person who is not involved in RE or who wants to maintain a balanced asset allocation and be involved in equities/fixed income, a 401K is a no-brainer, particularly if you get employer-matching which is literally free money.Moreover, if you are interested in retiring early, you can always do a 72t to get your income a lot sooner and penalty-free.