In fact, if one takes the word "elect" in the sense that you've put it (The Jews were certainly the "chosen" people -- but chosen to spread the Gospel. It was their "chosen fate" to be the bearers of the Good News. Hence our Lord says "Salvation is from the Jews." In other words, they were chosen to do good works in faith and cooperation with God.), that makes sense.
Life is not a gift; it's a loan. God put us on this earth for a purpose known but to Him. If life were a gift we had a right to, we wouldn't have to give it back, but we do.
As with any loan, we can do good with it, by multiplying and sharing His blessings (2 Cor 9:9-11), or we can squnder it on selfish, useless and idle things. Our nature tends towards the latter.
But, in giving us life and His blessings, God "elects" us. If we fail to make that loan worthy of His love, that is our fault.