The literal translation of 我为祖国的强大而感到骄傲 is "Because of [my contribution to] the strength of my country, I thus feel proud". You can only omit 而 is you substitute as a comma. This is to say, the sentence must be written as, "我为祖国的强大, 感到骄傲" so when you speak it, you must have a pause. 而= hence, so, thus in this context. Also this is semi-Classical Chinese where such particles can be used as punctuation marks for emphasis on certain grammar structure. A modern way of saying is, 我为了祖国能够强大, 我感觉到骄傲. Also it be interpreted as, without your contribution, you won't feel proud. This is not what a native speaker would mean. Better to write as, 祖国之強而令我骄傲. Omit 大 because it implies expansionism through power and strength!

Hi, Justin. I think these two sentences below make sense to me. 我为祖国的强大而骄傲 我为祖国的强大感到骄傲 「我为祖国的强大而感到骄傲」is a bit redundant, though it's correct. More examples: "I am proud of my job." = “我为我的工作(而)感到自豪” "I feel sad about their divorce." = "我为他们的离婚(而)感到难过" With all these examples, I think "而" means "so.." or "as a result.." something something something..., so I feel proud of it. And BTW, to avoid misunderstanding of「骄傲」, you can use 「自豪」instead of 「骄傲」when you are saying something positive.

of course 而 can be omitted , adding 而 is an old style of writing

Yes, both are correct. Yes, omitting the "而" is fine, but do read on. 我为祖国的强大感到骄傲。 I'm proud my country is strong. 我为祖国的强大(而)感到骄傲。 I'm proud (that) my country is strong. In both cases, the 而 and the "that" can be omitted. 而 is just there to explicitly indicate to the reader that the reason for your sense of pride is whatever you stated at the front of the sentence.