Old Earth theory is wrong for multiple reasons.
But, it doesn't matter. What matters is does a person know Christ as the one true God, and do they seek to be more like Him.
As far as old earth vs young earth, its a debate where neither side can see eye to eye.
But here is why I believe in young Earth.
The gap theory is irrelevant, the Bible explains the order of creation in an opposing order as to evolution.
The Flood was not a local event, but a global one. Just as our Salvation is not local but Global.
An old earth dating relies on methods proven to be in accurate beyond measures. (C14 dating)
We have Tyrannosaurus skeletons with live bone marrow still in them, completely impossible in an old age earth due to half life's.
You cannot have death before man's sin.
The "asteroid theory" is death by fire when Christ is the only time the world will die to fire.
And many more.
The old earth believer will discredit or explain away many of these things just as I would do to them. The biggest thing is, do you firmly believe in Christ.
Personally I lost my faith when reading Genesis for the first time, as the contradictions with evolution were so massive I discredited the Bible instead of evolution.
It took a little longer than a year of God showing me John Lennox, Kent Hound, and Chuck Missler... for me to accept the young earth model.