Training is a bad word

On the other hand, building capability to enable a strategy and change results - that is powerful.

I often hear managers say their people need more training or they need a training budget.

The first step to influencing the organization in a new direction is to abolish the word training.  Training budgets are easy to cut.  Training is a tactic and I've rarely been influential talking about a tactic.  

Instead, talk about the strategy first.  Then how you'll build capability, or develop people, but not training.  Finish with the results it will create.  First 'why', then 'what', finally 'so what'.