I'm a vegetarian but my mother cooks with garlic and onions. Why are they in the tamasic ("mode of ignorance" – unofferable to Krishna) category?
Hare Krishna! This is a very common problem. My son in law is Punjabi and his family also cooks with garlic and onions. It can be troublesome. Actually, garlic and onions can't be offered to Lord Krishna, and that's why devotees of Krishna don't eat them. Buddhists also consider garlic tamasic because of its strongly pungent odor. There are histories in the Puranas that indicate that the Lord created onions in such a way that we cry when preparing them, just to show us that He's not happy when we eat them.
Actually, when you think about it, giving up these two items in order to make Krishna happy isn't a very great sacrifice. To eat sattvic ("mode of goodness") food, to offer that food to Krishna and honor the prasad ("mercy" - food offered to Krishna) we simply have to give these two small items up. Living without garlic and onions is quite easy actually, but the problem is compounded with the fact that your mother cooks with them.
When my son in law's mother cooks for us, she leaves these items out. We then offer everything to Krishna, purely, and afterwards she separately adds some garlic or onion pickles to her food. That way, we're all able to eat Krishna prasadam, and she can eat what she wants.
Eventually, if you want to make spiritual advancement, you will give these items up. When that happens depends on your determination. But Lord Krishna will be pleased if you can make the sacrifice.
I hope this is helpful.