Angels are spirits.
Humans are souls.
The physical body (no pun intended) is immaterial. Its the inner being that makes a man a man, and their spirit is what makes and angel an angel.
So... man can not become an angel. And, an angel can not become a man. Yet angels in the Bible have the appearance as a man. Its the inner spirit that makes an angel different. But, a man, being a soul, can become 'like' an angel in regards to having everlasting life.
Its the Resurrection body that will make our soul immortal. For its the physical body that can now die,. The soul continues on. The soul has everlasting existence. Having what kind of body is what gives a life that will be either mortal, or immortal.