If instant messaging such as skype, messenger,imo etc are safe to use, then why are there leaked video calls posted on pornsites and youtube?
Secure channels vs secure endpoints
A secure communication channel allows you to communicate with someone else without third parties being able to intercept or modify the messages, no more no less.
They don't protect the communication from the intended recipient - they can record the conversation and redistribute it, and this is a major source of leaked private videos.
They also don't protect you if the endpoint is compromised - the sending or receiving device may record everything being shown on the screen.
Define "safe to use".
For instance, we call cars "safe to use" but that doesn't imply as a driver you can't run a pedestrian over.
Likely what you have misinterpreted is the fact that the transportation of messages is "safe to use", but doesn't mean the recipient will follow suit. What they end up doing with the messages is anyone's guess.
With Facebook and other social media websites, it is unlikely that the corporations who run such services can view/read/edit messages. This again doesn't mean a recipient would be unable to view/read/edit messages. The "endpoint" is not secure, as it's just a normal web browser.
The first thing that bothers me is the unsupported claim that instant messaging services are “safe to use”. As with any decision in life, you'll first have to define what values you are concerned about and what degree of risk you are willing to accept for them. Then you can evaluate whether a given solution is “safe to use” for you in your situation. It is certainly not the case that all messaging services are suited for all people's needs.
Here are some reasons why private video chats might get “leaked” on the internet. (In order of decreasing likelihood as per my perception.)
Indiscretion on behalf of your communication partner. Seriously, I'm very confident that this is the number one reason for the kind of incidents you're concerned about. On most setups, it is easy to capture your monitor and audio even if the messaging service doesn't provide this functionality out of the box. And even if it were not, you can always physically film the screen although that might be somewhat difficult to hide in a duplex video chat.
While it ought to be different, mutual trust between the partners in many sexual relationships is not very high (often much lower than between close friends) and personal respect and responsibility for the partner's rights of personality often leaves much to desire. Moreover, delicate conversations might especially occur in times where their relationship is not in the best state anyway.
In case the video is stored permanently on either of the partner's computer (whether by mutual agreement or not), factors outside of the messaging service may cause that file to get into the wrong hands. After all, it's just a file on a disk and other people can read it if the computer is infected by malware, left unattended or the (unencrypted) storage media is finally disposed. Many people also use “cloud services” to store their data which opens up a whole new attack surface.
If either of the parties computer is infected with malware, it can replace the messaging client with a compromised version that looks identical and appears functional to the user but redirects a copy of the video stream to the attacker's server. Alternatively, it can leave the video client alone and capture video output at a lower level. Such malware is used by the police and intelligence services in many countries for telephone tapping. It can certainly be used by civilians, too.
The video traffic might not be protected using end-to-end encryption, might not be encrypted at all or the encryption might not be implemented correctly. Until recently, few people would pay attention to this fact. If the software is proprietary, we cannot know for sure how it implements cryptography, even if the provider claims it does so properly. And it can certainly change with every update. The EFF publishes a “Secure Messaging Scorecard” with what is known about the more popular messaging services. Check it out.
If the traffic is not encrypted at all, then anybody who gets access to the network traffic can read it. This includes the network operators in your home if you, say, live in a student's apartment where you don't manage this infrastructure yourself. When using unencrypted wireless communication, anyone who is within the reach of the signal can listen. Many networks still use poor encryption or none at all. Your internet service provider and the government can always read your unencrypted traffic.
If the traffic is encrypted but only between the servers and not end-to-end, then the service provider can read all your traffic and give anyone access to it. While this is certainly used by intelligence and law-enforcement services, it seems unlikely that they would abuse their power to upload private video communications to porn sites which is illegal and endangers their business reputation. Governments might resort to such tactics in order to degrade the public reputation of a person when they deem it worth it but we can assume that this doesn't affect many people. But even if nobody is willingly abusing the data, it is worth noting that if the provider's servers can see the traffic in plain text, an attacker can also try to attack those and suddenly get access to many people's communication.