First - Buying land where they are is a good way to lose their shirt. Job turnover and high purchase price makes renting-near-work a very attractive thing to do for bike-riding and cost-saving in general.
Second - Borrowing against your pension for a down payment on a fluctuating asset? You have to be kidding me.
Third - Two teachers attempting to purchase a $300,000+ home? Are you kidding?
Fourth - Almost all of the people in the teaching-to-pay-for-your-masters program that they are in burn out after 2 years or so (I know from personal conversations with 10+ people through this program). This doesn't exactly scream "I will stay in this location for five years". This is terribly risky.
Fifth - on Page 2, it says that the income is unstable. Are they seriously looking to make a 30-year commitment with unstable income? "Stretching" their purchase price? This sounds like a recipe for bankruptcy/default.
Sixth - the paid thousands in broker's fees to find a rental? WTF?
Seventh - They mention that the DOWN PAYMENT is 1 year's combined salary. This is scary. They are buying too much house (my down payment was 60% lower). Why do they want a house so badly?
Eighth - They can make a map of the city's happy hour? Seriously?
Ninth - They decided to rent a house which is a 3-hour commute away? Do they LIKE commuting? I understand that the 'all you can ride' fare pass in NYC is available, but I cannot imagine paying for that with three hours of my time. This is 1/8 of the day. If you assume 8 hours work (yea, right!), and 8 hours sleep (yea, right!), with 30 minute meals twice per day (instant meals!), and 1 hour of getting-dressed/showering/shaving/whatever, 88% of their day is already spoken for (3 remaining hours).
Tenth - Why are they trying to BUY A HOME in NEW YORK CITY? Have you seen a map of NYC? It is made up of large buildings. Apartments and condos are the fare of the day.
Finally - Is this supposed to be a sob story? Teaching couple in NYC is not presented with the option of 'home owner'. Is this a shock? Highly volatile market, unstable career, borrowing against 401K, city generally unfriendly to home ownership, and a series of general 'red flags' in their finances all contribute to saying "this couple should not own a home".