I agree that it's not totally about saving money, although that is part of it. Your upfront costs can be high enough that you won't see any real savings for a few years, and you really would only see significant savings if you're comparing to free range/organic/pastured/etc chicken (ie if you're comparing like to like, so if you compare how you raise your chickens to a comparable product at the store, not the bargain chicken). A broiler costs around $1 to buy as a chick, and eats about 20 lbs of food over 8 weeks, so depending on the cost of your feed that one chicken is going to cost you (based on these expenses alone, not anything involving housing, etc) between $6-$9, possibly higher if you feed organic or lower if you get a good deal at a feed mill. Bargain basement on sale chicken tends to be $4-$5 a bird, but it is an inferior product. Comparable birds in the store, not even organic, are $12 and up.
So yes, comparing like for like you'll save money over the course of several years. But there's also the satisfaction and pride of doing it yourself, and of knowing that your food was raised humanely and fed whatever you're comfortable feeding.
So far as "not being able to do it," I had the same reservations. But someone else who has chickens near here told me she takes the chickens to a locker to be processed, so I took the plunge and bought 10 Cornish Crosses when I bought my laying chicks. Now having lived with these birds for three weeks I'm starting to think that I may have no problem processing them myself (although if I can pull it off I may have my hubby do the killing- I don't want to do it, but if it comes down to it I feel like I could). For the second week I had them I was like "I don't think I'll do broilers again- they're so gross and ugly and have no personality," ...especially compared to my ladies and my three roosters. But then I realized that that is PERFECT (except for the gross part- but I built a tractor for them so it's not bad now). You don't get very attached to the (all due respect to them) fat lazy uniformly colored eating machines that are Cornish X's. They eat, they waddle over to the water, they poop (a lot...), and they lay down. So now I have much respect for them as animals (hey- besides giving me meat in a few more weeks they're also fertilizing my lawn for free!), but I don't think I'll have any problem doing the deed if I have to. That's my two cents, anyway (and I'm a bleeding heart animal lover).