In this video, it stated to not speak about nightmares at all and don't narrate them to anyone.
Why is that? Is there any problem with that?
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Because there are narrations about the Prophet instructing us not to do so:
It was reported that Abu Hurayrah said: “The Prophet (peace and blessings of Allaah be upon him) said: ‘If any one of you sees something that he dislikes (in a dream), let him get up and pray, and not tell people about it. (narrated by Muslim, 2263)
It was narrated from Abu Hurayrah that the Prophet (peace and blessings of Allaah be upon him) said: “Dreams are of three types: glad tidings from Allaah, what is on a person’s mind, and frightening dreams from the Shaytaan. If any of you sees a dream that he likes, let him tell others of it if he wishes, but if he sees something that he dislikes, he should not tell anyone about it, and he should get up and pray.” (Saheeh Sunan Ibn Maajah, 3154)
There might be other narrations that stating the reason but none that I came across so far.
The narration below, cited in this answer seems to state the reason, not sure if this is the only reason:
Jabir reported Allah's Messenger (may peace be upon him) as saying: There came to him (the Holy Prophet) a desert Arab and said: I saw in a dream that I had been beheaded and I had been following it (the severed head). Allah's Apostle (may peace be upon him) reprimanded him saying: Do not inform about the vain sporting of devil with you during the night. (Sahih Muslim Book 029, Hadith Number 5640)