Did you hit your mash temperature?
If your mash temperature was high, maybe you have more unfermentables than you had intended. When estimating FG, one of the
things that BS assumes is that you hit your mash temperature.
Did you make a starter and did you have a high enough yeast cell count for the brew?
If you underpitched your yeast, they will be a little stressed and may not have been healthy enough to finish the job. 1.060 SG isn't
too high of a starting gravity, but it is high enough that I would have made a starter.
How old what your yeast packet?
If it was old enough and you didn't make a starter, you underpitched. There are yeast calculators (Mr. Malty being one), that can tell
you approximately how many viable cells are actually in your yeast package, based on the date it was packaged.
Did you use yeast nutrient?
I always use yeast nutrient, to make sure that my yeasties have what they need to build solid cell walls and multiply well, so that
even if I slightly underpitched, they will have what they need to make up for anything that I didn't do perfectly.
Did you oxygenate your wort really well?
During the first phases of fermentation your yeast need a lot of oxygen to get healthy and make lots of baby yeast. If you don't give
them enough oxygen, they won't be at their best and will be stressed after they use up what little oxygen they start with.
Think of it not as making beer, but as growing a vibrant healthy yeast community in your fermenter. If you put enough yeast in that community and give them all of the things that they need, they'll be much happier and much more productive.
However, if you give them a big job (eating a lot of sugar and making alcohol and CO2) and don't put a large enough supply of workers there to do the job, and don't give them the tools to do the job properly, they'll get stressed out and won't finish the job.