You've answered your own question.
You believe that there might be some truth in what she said.
Nothing is offensive, we hear words, observe actions, and attach meaning to those words or actions. We can choose any corresponding emotion, if something "is offensive", we have chosen to find it offensive. We have considered the circumstances and decided which emotion to feel.
When people choose to find things offensive, it's often as a result of an identified "failure" which they have identified in their own lives. For example, a overweight person who feels unhappy with their body may choose to find any comment regarding their weight as offensive, as it forces them to consider an aspect of their own personality which they have issues with and which they have been trying to ignore.
You have been thinking the same as your mother, but she voiced the opinion first and now you have been forced to think about it.
It's a normal, if unhelpful, facet of human behaviour.