I think in the Western world age has become something to be embarrassed about, sadly. The Bible says that in Job 12:12 "wisdom is with the aged, and understanding in the length of days." I think back then age was something people revered and considered good. If someone lived to be of a certain age, he/she was considered blessed and highly favored.
Now it's all about looking and feeling young. There's a stereotype of older people being sick, unable to control their bladder, or just grouchy. I don't think this is all true, but it's a stereotype nonetheless. Whereas young people are considered attractive, active, healthy, and happy. Ironically I think it's quite the opposite. Lots of young people (millennials and the teens) are very unhealthy and very depressed.
I know a man who's about to be 85 and he's amazing! He was married to his wife for over 50 years until she passed away. He works in a farm on his own and reads the Bible every single day. He's read it three time this year alone! I know all this because he was in the newspaper. How many of us millennials or those younger, would be able to say that? The way things are looking, not very many.
Also, our society puts a huge emphasizes on looks. Most women and even some men are unhappy with the way they look. Of course if you're just looking at the exterior, younger people will look better. But if you look at everything (especially the heart), most of the older generations are way more beautiful than the younger ones today. After all, understanding and wisdom are beautiful traits that everyone can appreciate!
So yeah, I think that's why they get offended. I'll be 27 in Oct. and that gives me three more years to be in my 20s. I'm a little sad about it but then I stop to think that God loves me just the way that I am. Why should I have to worry about aging? Everyone is aging everyday. People in general just need to let go of what the media tells us. We need to find our confidence in Christ.
Maybe that's why a lot of people get offended too? Since many don't believe anymore, they don't even know where to find confidence, self-esteem, and worthiness. Kinda sad to think about.