my one pet keep having their training on Strength .. at what stage does it changes??

my pet Axol have everytime their stats changed in training ...

The stats should change after every training session. The higher your pet's tier the longer it takes for a training session to complete.

MetalGarurumon keeps training his Strength..

while Axol with each session trains a different stat

You can only train your other stats to 2.5 times your pet's level, so if strength is the only option for training then it means your other stats are at least 2.5 times your pet's level. If you raise his level then you can train the other stats again

looking at your pet stats it seems that MetalGarurumon over trained on Level. So you will be offered strength to train until the pet strength reaches 107 or 108, then you will be offered the next stat until it reaches 107 or 108, and so forth. That said you can manually choose another stat to train, just click the drop down and pick which ever you want. This will continue to happen until your stats "catch-up" to the level.

I'll tell you to save sp overall only train level when other stats can't go more. Higher the level higher the cost to train all the other stats. So level when needed then get it until the others can't grow more then train level again In early stages the best tactic is MANUAL level train and use auto training(when possible )for the other stats like strength.