What made Jesus question at Mt 21:25 a good example for Christians or was it a bad question because the Jews could not answer?

While the text does not say, I believe their motivation was, “If he says ‘from God,’ we can prosecute, and if he says anything else, we can veto it because we’re the leaders.” Jesus stuck them with the dilemma they thought they would stick Him with.

Jesus saith unto them, Verily I say unto you, That the publicans and the harlots go into the kingdom of God before you. For John came unto you in the way of righteousness, and ye believed him not: but the publicans and the harlots believed him: and ye, when ye had seen it, repented not afterward, that ye might believe him. [Matthew 21 :31,32 KJV]

There was nothing difficult at all about Jesus' question. Either John was, or was not, sent of God, as John tells us he definitely was :

There was a man sent of God whose name was John [John 1:6 KJV]

Was the baptism with which John baptised of heaven ? Then receive it, welcome it, and believe in him to whom John pointed :

Make straight the way of the Lord [John 1:23 KJV]

Behold the Lamb of God which taketh away the sin of the world [John 1:29 KJV]

And I saw and bare record that this is the Son of God [John 1:34 KJV]

But they did not repent. And they did not believe.

Why not ? Because it was not of heaven ?

But they would not be drawn on whether it was, or was not, of heaven.

We cannot tell.

But this was not ingenuous. Later in the chapter, Matthew records the real reason for their not following John, and then Jesus :

Come, this is heir, let us kill him [Matthew 21:38 KJV]

They wanted the things of God for themselves. They wanted to retain their religious hierarchy, their religious position, their self-righteousness. This is what Matthew's book is all about : the inception of the kingdom of heaven and its rejection by a religious kingdom on earth.

Clinging to what had, originally, been established by God (but only as a pre-empting of something far greater, they rejected John, they rejected Jesus, they followed not the publicans and harlots who repented and believed.

And in the end, they crucified the Lord of Glory. (I Corinthians 2:8 KJV.)

Hard-hearted and unbelieveing to the end, the rejected every approach by God and they shunned every means that he gave for them to obtain eternal life by Jesus Christ.

Jesus' question exposes them for their hypocrisy. Nor does he leave it at that. He pursues after them, with a parable which further lays bare their true spiritual state.

What made Jesus question at Mt 21:25 so effective or was it a bad question because the Jews could not answer?

Answer: The question was effective, considering:

1. The context of the question (Matt 21 - 23), which is part of the narrative purpose of Matthew, i.e. Jesus's confrontation with the Religious Authorities of Jerusalem to expose their stubbornness and hypocrisy, which Matthew then used to show their guilt in executing Jesus

2. New Testament background about how Pharisaic argumentation worked

Jesus's counter question was effective because Jesus outsmarted the true intention of the Pharisees by beating them at their own game by being a better debater.

First of all, it was the Pharisees who asked the question FIRST in Matt 21:23 (ESV) after witnessing 1) Jesus entering Jerusalem as a King (although entering in peace by riding a donkey), 2) Clearing the Temple, 3) Miraculous withering of the fig tree:

By what authority are you doing these things, and who gave you this authority?

It was a fair question, but also an unnecessary question if they believed John the Baptist's pointing that Jesus was in fact the Messiah sent by God the Father, the same God who sent John the Baptist as a prophet. Please remember that by that time Jesus had performed enough miracles already to authenticate his claim.

Jesus's asking a question in v. 24-25:

I also will ask you one question, and if you tell me the answer, then I also will tell you by what authority I do these things. The baptism of John, from where did it come? From heaven or from man?

in response to the Pharisees's question in v. 23 is perfectly fair game in rabbinic debate (see R.T. France's commentary on Matthew):

A counter-question in place of a direct answer was an accepted pattern in rabbinic debate, where the second question further opens up the subject raised by the first. We have seen an example already in 15:3, and another will follow in 22:20; cf. also Mark 10:3. In none of these cases does Jesus' counter-question change the subject, but it substitutes dialogue for simple assertion and so answers the question more obliquely where a direct pronouncement might have been used against him.

The dilemma of the questioners is not an intellectual one—their view of John seems to have been clear enough—but tactical, involving the danger of “loss of face”. To voice their true view of John would have exposed them to popular anger, but to give an insincere answer would expose them to ridicule, since their rejection of John’s message was well-known, as Jesus will confirm in v. 32. While there is some ambivalence about the popular response to John as Jesus describes it in 11:16–19, the presupposition is that they went out to him as a prophet (11:9), even if his style of prophetic ministry proved not to be to their taste. John’s prophetic image is confirmed in 16:14, and his popular appeal, already mentioned in 14:5, is presupposed in v. 32.

As for the sub-question:

Was it wrong for Jesus to ask what he knew they could not answer because of the parameters of his question?

It was neither wrong for Jesus to ask nor was the question unanswerable. Jesus's counter question was tactical to expose their insincerity in being the shepherds for the people of God AND Jesus didn't have to answer an impertinent question. They admitted defeat at the debate because they were afraid of the public if they declared their true view that John the Baptist wasn't a true prophet.