You omit, doc, that going from 30 to 15 saves immensely the total interest payments amounting to thousands. 30 to0 40 is tantamount to a 3 yr car loan and a 5yr which means hundreds monthly; translate that 30 to 40 and monthly payments are reduced dramatically.
Yes you do save a ton in interest, but your monthly payments do not change much. And that is the problem, not how much interest they pay, but how much they pay each month. The car load is not valid. You are going from 36 months to 60, a 67% change and most of the payments are principal, not interest. A 30-40 year change is only half that, and most of the payments are interest, so you are not reducing your interest paments until year 18 or so (on the 30).
There are calculators on the internet. Check it out: 30yr, 6.5%, 250,000 - payments $1580
40yr, 6.5% (it would be higher because of the longer term, but let's keep it the same), 250,000 = 1463.
Simple math.