It's hard to separate them, but they are different. 'To' is used in many many ways that towards can not be used. Towards means only 'in the direction of' or 'progressing / promoting a goal'
This sort of use is not interchangeable:
I'd like to show you something
it's difficult to explain
Where is is interchangeable, there is a difference in meaning
'I am going to the city' - I am travelling, my destination is the city. I will not stop until I reach the city. My purpose for moving is to reach the city.
I am going towards the city - I am travelling in the direction of the city. It would be my destination, if i keep moving. I am describing only my current motion and direction.
Why would this matter? There are many times when you would choose to describe the direction of travel, without implying that the journey will be completed. 'He threw the ball towards the goal (but maybe it did not reach it)' or 'he threw the ball to the goal (at the end of the throw, the ball reached the goal). Another example: I was running towards the shop when i bumped into the man (the journey was interrupted)
I don't know the context of your correction, but your original statement is basically 'Governments should give support to schools.
After the correction, it means this:
'the government should give support (to students) towards (the goal of achieving) higher education'.
Because towards implies a goal or destination, and the school alone is not one, the meaning of higher education changes to a goal. Because it is a goal, it must belong to someone. Therefore, both of these things are implied by the use of the word 'towards'.