In Mathew 19:5, how do they become one? If they are one and yet they are two, do they lose their identity?
In Matthew 19:5, Jesus is quoting: "Therefore a man shall leave his father and mother and be joined to his wife, and they shall become one flesh" (Genesis 2:24). The Hebrew word 'echad, is translated as "one." This word can refer to a quantity, such as in Genesis 2:21, but usually it is used to express the idea of unity. We do the same in English when we say, "We have one heart!" If you took such as statement literally, it would be a contradiction since "we" is a word indicating many. The idea of unified or compounded oneness is clearly seen in: "And the LORD said, "Indeed the people are one and they all have one language, and this is what they begin to do; now nothing that they propose to do will be withheld from them"" (Genesis 11:6). People can act together and be one without losing their individual identity.
In a marriage, two people, a man and a woman, join through a covenant to form a family. Two separate people with separate lives, join together in one purpose and to have one goal. They are still individuals. They still look at life in slightly different ways. But they pull together to work together as a single unit.