Please, explain the reason the following sentence is wrong.
We don't have any news about him until now.
In the first part of the sentence, "We don't have any news about him", "don't" is used in the present tense meaning we currently don't have any news.
By adding "until now" to the sentence tells the reader that actually we do now have some news.
This is a contradiction. We can't currently have no news and have some news.
You could reword it as:
"We hadn't had any news about him until now."
The use of "hadn't had" in the past perfect tense tells the reader that that situation had existed but has now ended.
We don't have any news about him until now.
Cambridge Dictionary explains the tense to use for Time up to now.
We use the present perfect to talk about time up to now, that is, events that took place in the past but which connect with the present. The present perfect is often used with time expressions which indicate time up to now:
I haven’t seen her since January 1995.
We could hence consider
We have not had any news about him until now.
"Until now" refers to the past, but your sentence is in present tense. You could say something like
We haven't gotten any news about him until now.