In my case, the people are not changing their opinion. Their opinion remains the same, just they are bringing new arguments everytime just to prove that their opinion is correct.
A salesman who is trying to sell a big offroad vehicle may argue that you should buy this, because, you could use this vehicle during your adventure. Now, you said that you live in a busy city and there is no way you could bring this vehicle to your next adventure. Besides, you do not like nature (I don't know why he hates, though). So, the salesman changes his point and says that this is a 7 seater car and you could bring your entire family. So, you said you live alone. So, he change his point and says it has large storage space.
Here, the opinion has not changed. He still wants you to buy the car. He just change the reason.
Some other example would be
You went to a repair shop to repair your laptop's screen. You were suppose to get a low resolution, high refresh rate screen. It was a deal between you guys. But, they messed up and gave a high res, low referesh rate screen. Since, you have already paid for the repair, you want refund, since this was against the deal. Now, he would say that we would have given the refund but, we never had such deal that said you'll get low res, high refresh rate screen. So, you show them the transcript of the conversation. Now, they'll say that, this was never the issue. Since, the replacement box does not explicitly mention the resolution and refresh rate, so how would they know. So, you showed them the serial number on the box and a simple internet search shows the specs. Now, they will give a new reason.
Similarly, when people make mistakes they give reasons to justify their action, even when their previous reasons were proven incorrect.
This example could be extended to other senarios as well. In the political scenario, this could be that ruling party brings a bill to the parliament, but the opposition opposes as it contains some error. But, once it is proven it didn't, they'll raise another issue.
In the college basketball scenario, the coach who doesn't like you will give have difficult test for your selection. Even if you did great in the previous test
In a sentence, it would be used as,
You're a ______ person
___ person tend to go to extreme cases to prove their point