What do you mean time is irreversible? Your movement in it is irreversible, just like your movement on a one-way road is irreversible in space. Time itself does not possess the property of irreversibility, at least in modern physics. All the equations describing natural phenomena can work both ways, forwards and backwards in time.
Maybe this analogy will be helpful for you. We have CPU with mutable RAM. You can create immutable language on top and start arguing that you can go both ways in mutations back and forth in RAM. But this is the feature of the abstraction you applied not the core feature of "reality".
This is what differs model from reality. You're talking about abstract concept which helps you to measure mutations but as I tried to explain above - is not a real thing. It's just working and useful idea.
