This is the 17462nd most frequent Russian word.
тобою
"Тобою" means "by you" or "with you" (instrumental case of "ты").
In this example, 'тобою' again takes the instrumental case to convey the entity being compared.
Нам не сравниться тобою.
We can't compare to you.
In this sentence, 'тобою' is used as an instrumental case form of 'ты' to express the means or instrument of pride.
Я горжусь тобою.
I am proud of you.
Here, 'тобою' is in the instrumental case, denoting 'by you' in the context of passive voice or action performing subject.