embedding random videos to your website

I have a website that specialized on a certain niche and a lot of my articles have videos from other people on youtube embded on the article as examples for the readers.
and lately I organized all of the videos on a page. as a gallery of all the available videos on my website. and some people started to comment on my website saying that these videos are not mine because you can easly see that they are from all different kind of channels and that what I am doing is illegal.

I myself don't think it is illegal or that they could sue me or anything like that (I hope so) but I am just concerned if youtube could force me someday to take all of the videos from my website or block embded videos from youtube to show up on my website.

please if anyone have information about how does this work or if they had a similar experience like this before tell me what should I do to avoid these problems.
note:
I only embed I never reupload

embed videos are not illegal just ignore them. if they don't want you to embed these videos they have an option on their channel to close embed on websites which means there is nothing illegal and what you doing is totally legal.

you are getting them views, tf they complain about?

Sosolapute said:

you are getting them views, tf they complain about?

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exactly I may have used some of their videos to give example of bad practices and criticized them but, no harm was done to them personally and they got more views because of me

mrgreengreen said:

exactly I may have used some of their videos to give example of bad practices and criticized them but, no harm was done to them personally and they got more views because of me

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So you are using their videos to illustrate bad practices and criticizing them, and you don't understand why they are complaining about you? Perhaps you should consider trying to make
friends first before starting fires with those who may become enemies. To clarify, if you aren't creating your own content, then at least embed content that shows what positive things you
like about someone's videos and praise them for it. Show examples of good videos, and just tell your viewers to avoid doing the opposite. You don't actually have to show any bad videos
at all. You will be making friends instead, and then you will stop getting complaints.

Castlevision said:

So you are using their videos to illustrate bad practices and criticizing them, and you don't understand why they are complaining about you? Perhaps you should consider trying to make
friends first before starting fires with those who may become enemies. To clarify, if you aren't creating your own content, then at least embed content that shows what positive things you
like about someone's videos and praise them for it. Show examples of good videos, and just tell your viewers to avoid doing the opposite. You don't actually have to show any bad videos
at all. You will be making friends instead, and then you will stop getting complaints.

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I am really thankful for your advice and I think it is a really good one and wise thing to do, but in my case this is what people likes about my website and if the other way was working I would love to do it. but at the moment this is where the money is for me.