Several reasons not to mix an old and new battery, but a major one is that the old one will kill the new one. Here is how it can work: a cell in the old battery goes bad. Your charger, even a smart one knows to charge at a certain voltage. If it sees voltage is low because of that bad cell, it will keep charging the batteries. This OVER-charges the good battery. That is why battery failure is often accompanied by batteries boiled dry and swollen cases-- severe overcharging.
The reason for not mixing battery technologies is that each has a "preferred" charging algorithm. With a properly programmed smart charger or smart inverter/charger is can be specifically tailored to a battery technology.
This does not mean that you can't mix a new wet cell with new AGM, as their charging algorithms are pretty close, but it is not the ideal setup.