1. From reasoning: It requires the possibility of a very short and artificial past.
Suppose you say that the universe is young but was created to look old. And by "young" you mean "a few thousand years." By allowing that possibility, you also allow the possibility that "young" could mean "a few seconds." If that was the case, then all our memories from more than a few seconds ago would be implanted there by God. Furthermore, it would also mean that the historic events of Jesus' life never actually happened, but God has created an artificial history that indicates they were. No Jesus, no crucifixion, no atonement. So, to allow a universe that is X years old but artificially looks like it is Y years old, with Y larger than X, is to allow some far-fetched possibilities.
2. From textual analysis: The writing styles of Gen 1 and 2 are vastly different to each other and to the rest of Genesis, and bear a striking similarity to other creation stories.
So what? Here's what. It means that they oughtn't be read as the same genre as the histories (e.g., Kings, Chronicles, etc.) but should be treated as parables or allegories. They are simply too different to be read as any kind of history.
3. From science: There's only one truth and scientific method is pretty good.
It would be strange and non-sensical if God created a universe with one truth and then gave a revelation with a contradictory truth. What we learn about the universe through scientific method isn't a threat to God, but is a way of rescuing us from superstition. It takes away from God the attributes that we have ascribed to God and allows us the space to focus our religious efforts on what really matters.
And just in case that was even in any doubt, I go back to Jerome's account of John the Elder.
The Blessed Evangelist John lived at Ephesus down to an extreme old age, and, at length, when he was with difficulty carried to the Church, and was not able to exhort the congregation at length, he was used simply to say at each meeting, My little children, love one another. At last the disciples and brethren were weary with hearing these words continually, and asked him, Master, wherefore ever sayest thou this only? Whereto he replied to them, worthy of John, It is the commandment of the Lord, and if this only be done, it is enough.
What matters is this love, not quarrels about the origins of the universe. However, it seems that there is no end of questions about it.