Am I acting irrationally when I’m saying I’m not ready for marriage?

move to a country that isnt stuck in medieval times

you're an empowered woman. you don't need a husband. 

You people need to stop your culture bs, and move into the 21st century, get out of the sandals  and the sand

YOU, in theory, know what is best for YOU.  That might involve marrying this man.  It might involve not marrying this man.

If you can't make your own decision, if you need the input of strangers who do not understand your culture, then don't marry anyone.

You're not irrational. But if this your family's culture and you're in any way financially dependent on your parents you may have to either go through with marrying this stranger or become independent fast. 

Oh Dear! Remind your relatives (etc.) this is 2020, not 1820! Things have changed a lot in almost every way. Life expectancy, for example, has improved a lot: once people married young because so many people died when young, in childbirth, etc. You are your own person and calling you names is childish! 

Sure - get to know him, but remind him that you are not looking to marry him at the moment, and you don't need to. Make an agreement with them that you won't try to interfere with their lives and they can do the same.  

Good Luck!

I think you're running across a generational clash, where the older generation has a certain set of values that have (more or less) worked for them and have facilitated societal cohesiveness, whereas the younger generation is more embracing of values around individual choice and happiness over filial piety. Both philosophies have their benefits and drawbacks. Westerners (Americans in particular) are generally more individualistic and will say that you should do whatever you want to do even if it means your family disapproves, but Easterners are more prone to believing that this view is too self-centered and leads to social chaos and disorder. Individualists don't like their rights or choices stepped on, which can sometimes lead to valuing short-term wants over long-term gains, and traditionalists value stability above all else, even at the expense of personal happiness.

All of that said, though, what do YOU want out of marriage? Would you be content with a partner who simply goes to work and provides while you manage the household, and you get along well enough to build a stable life? Or do you want someone who will be more of an equal partner and friend, without rigid division of gender roles, even if it means sacrificing other things (like financial comfort or social approval)? The latter sort of relationship, or "love" marriage, can bring great joy and personal fulfillment... but it's also harder to get right, because you're constantly having to communicate, compromise, and adjust expectations, which makes it crucial to try to pick the right person in the first place. And you have to do it on your own, because no one else will belong in the marriage besides you and your husband. If the former is what would make you most content then passion may never play much of a role in the marriage, but if you're okay with that, then letting your family help you pick a good partner may the the route to take. Their life experience may be helpful in identifying someone likely to be responsible, reliable, and stable over the long-term.

Don't listen to your parents and/or friends.  Don't even think about marriage until you both love and are in love with the person you intend to marry.  If you don't get turned on every time you think of him, if you don't feel empty inside when he's not with you...you should not be getting married to him.  There is no trigger age beyond which you should not get married.  Even old people get married.  So no rush.

No but I think it is irrational for a parent to expect their daughter to marry someone just because he decided he is interested and wants to get engaged and married to her.

They don't know better and you should wait until you are ready. Go with your gut and don't let anybody persuade you otherwise. They did what they did when they were young and are trying to force that on you because it's normal to them but this is a new age and that's not normal to you