'to push ahead' with a plan or arrangement means to continue with it when there are problems or others wish to stop.
- We've had a few problems but we have decided to push ahead.
- They are pushing ahead with plans to build the motorway despite the protests.
'to push around' means to tell someone to do something in a rude way.
- When I was young I was pushed around by my big brother.
- Don't push me around! I'm fed up of you telling me what to do.
'to push back' means to delay an appointment until a later date or time.
- It'll take an hour to get there. Let's push the meeting back until ten.
- My operation was pushed back a month due to a shortage of nurses.
'to push for' means to try to persuade someone to give you something.
- The assembly line workers are always pushing for a salary increase.
- The local residents are pushing for a lower speed limit to make the roads safer.
'to push in' means to jump into a queue in front of other people who are already waiting.
- I was very angry when they pushed in and were served before me.
- Don't push in. Go to the back of the line.
'to push on' means to continue doing something.
- Even though the project was not going very well, they pushed on with it.
- I must push on. I've got a lot of work to do.
'to push out' means to force someone to leave a job or activity.
- He didn't resign from his last job, he was pushed out.
- I felt I was pushed out of the group because I didn't agree with them on everything.
'to push past' means to press roughly into someone as you pass them.
- During the race, I had to push past a few runners to get to the front.
- He was in a great hurry and hit me as he pushed past.
'to push through' means to get something accepted, often with difficulty.
- The government pushed the legislation through very quickly.
- The local council pushed through measures to improve the schools.
'to push up' means to increase something, usually a price or rate.
- The war in the Middle East has pushed up the price of petrol.
- The bad weather has pushed the price of some vegetables up by ten percent.