Unlike a condominium purchase, a coop requires an extensive review process which is, to say the least, subjective.
[to learn more about the differences between coops and condos, please check out my tutorial video: "Coops vs Condos: What You Need to Know" https://youtu.be/PS_4tRFqH4w
Basically, a coop Board of Directors can turn down a buyer for ANY reason, so long as fair housing laws are not violated. Meaning that if a Board member doesn't care for your choice of socks, haircut, or sports-team affiliation, you can in theory be rejected with no recourse.
In reality this is rarely the case - as it's in everybody's interest to attract good neighbors.. but there are no guarantees. I once had a buyer turned down who was one of the most qualified people I'd ever met. Successful physician, perfect credit, 7-figure income, all-cash purchase. Done deal, right? Nope! This particular coop had an issue with too many rentals in the building and a Board member felt that the potential purchaser MIGHT someday want to rent out the unit, so that was it.
I understood the Board's position. Banks don't want to be involved with coop buildings in which there are too many units being rented. The thought is that the fewer owner-occupants, the riskier the collateral. But as a broker trying to service my client, the seller, as well as doing my best for the buyer (a really nice guy), this just stunk!
[Some Manhattan coops have very recently become more flexible to attract would-be condo buyers, as demanded by shareholders seeking to widen the buyer pool and increase price per square foot (where condominiums command a significant premium over coops) . See related story HERE http://therealdeal.com/issues_articles/are-top-nyc-co-ops-in-panic-mode/]
Here is a really great article which clearly explains some of the most common reasons why potential NYC coop purchasers are rejected.