That is because time on earth is a relative value rather than a constant one. That is why we have 24 time zone on earth instead of just one.

Eg. A malaysian's 12pm is a New Yorker's 12am at the same point of time, while that same point of time is constant throughout the universe ever since the beginning of well. Time.

I personally believe time travel do not exist, all the existing time paradoxes sum up my argument.

My biggest doubt is traveling back into the past. A governing body that control time travel strictly? It will only take one single rogue time traveler to go back in past, causing event with powerful butterfly effect and create all kind of chaos.

With an infinite future, are there any guarantee that nobody else but the governing body develop time machine that's capable of traveling to the past? North Korea developed nuclear weapons too you know so what's there to stop countries that aren't on agreeable term with time traveling administrations bodies developing time machine and using them?

Time slowing down through high speed while proven possible but it's more of an illusion.

An astronaut slowed down 5 years of his time out of normal earth 10 years for eg.

So if he say, started his speedy journey at 2010, while he only aged 5 years, he still returns to Earth at the year 2020 not 2015. Since time is a relative value, it does give the illusion he traveled through time into 5 years ahead.

Don't believe in movie and shows Paradox and theory of time travel apply subjectively.

Take Terminator franchise. It is good example of time travel that defies paradox subjectively, meaning one person's paradox is applied while the other don't suffer from the effect.

In T1, the remains of Terminator were later used as research by Cyberdyne to lay the foundation for Skynet and other killing machines. The Terminator is from the future, so it becomes a loop with no beginning nor end, chicken and egg paradox.

John Connor wouldn't exist without Kyle Reese, and Kyle Reese wouldn't be sent back without John Connor. Another loop.

John Connor would have know that Skynet wasn't defeated when T2 ends. If Skynet cease to exist after he throws the chip and arm stolen from Cyberdyne into the molten steel. Why didn't the T-1000 vanishes? It won't take T3 to let John knows that Judgement Day is still there.
Time is actually a unit to calculate durations that's why it's relative (24 hour time zone thing) But, what is 'duration' then? They aren't made out of matters in the visible 3 dimension. It is said this 'duration' made up another invisible dimension that we couldn't see with conventional means. This is the place where time runs at a constant rate.

Do note that science beyond the 3 dimension is still an ongoing research(String Theory, The Theory of Everything), if I'd figured out to discuss it further I would've won a Nobel Prize already

Your father killing scenario has a paradox as well.

You kill his father, he wouldn't exist, why would you hate him? He doesn't exist! So what's drives you to go back in time and kill his father?

This is why I believe time travel doesn't exist.

I don't think that can be considered time travel because it happens in your subconscious. I think it's also known as Deja_Vu. I have experienced that before. In fact, I've heard of quite a number of people who have experienced it before. But I think topics like that come under metaphysics.