.... And nations?
Keep in mind that people who defend liberalism, use double standards and give much different definitions of it when speaking about their reasons for joining liberals.
  So what is the reason for it's being able to attract people?

There are many reasons.

Three quick reasons:

1) The first reason is the loss of faith and trust in traditional authority.  People become open to making individual selfishness a basis for existence when they begin to see the rest of the world as being fundamentally selfish.  

Rousseau: "man is born free but is everywhere in chains"

So how did men like Rousseau become so famous?

2) The second reason is the power of propaganda.  Liberalism has become powerful as the opinion making apparatus of the press and media came under the control of ʝʊdɛօmasonry.

People from traditional societies seem to be especially susceptible to outside propaganda.

3) The spread of moral corruption makes liberalism popular because people lose their natural moral sensibilities.

This is not only a reason but is a stage.  Eventually liberalism reaches the point it has in the West, where people no longer even understand the value of traditional morality, and no longer even understand the value of family, and have no patience whatsoever for traditional mores.

Why then people don't lose their trust in liberal authorities even after finding them as corrupt as traditional ones?

That's a very good question.  It is very noticeable that left-wing and liberal politicians are not affected by scandals the way right-wing politicians are.  People hate a corrupt right-winger, but tolerate and rally behind a corrupt left-winger.  I can't help thinking they sympathize with the wrong-doing of those on the left, even with someone like Stalin, because he has the same enemies.  These people support abortionists after all.

Even when a phony-rightwinger like Berlusconi is raked over  coals - there is a huge amount of indignation at his scandals.  And the look at the indignation over the scandals in the conciliar church.  But in the end, what are the consequences?  Because they are phony nothing serious happens to them.

People today sympathize with evil and hate good.

edit:

(and when a certain group becomes hated, they will be called right-wing, even when they are Communists.  For example the Soviet "hardliners" were called right-wing.)

My point is: Conversion from one idea to another is a slow process, the west didn't suddenly jump into liberalism. So, seeing that it only takes 30 years for a large number of people to shift from radical islam to militant liberalism makes me wonder!...

It is strange isn't it. A few cursory ideas in no specific order:

One possibility is that such accelerated liberalization is for that reason more superficial than the slow, deep, almost organic growth the counter-tradition has had in the West. In other words, maybe Bhutan (for instance) only has skin cancer, while America is terminal.

A second possibility is that time, understood as the succession of mental developments, is itself accelerating. So the decadence that formerly accreted over generations can now make similar progress in a matter of years.

A third possibility, indeed a likelihood, is that the liberals have more practice now. The technique of cultural revolution, in particular of propaganda, has been refined and habitualized over time, has had government money and scientific research poured into it, and as a result, has become much more effective and much more acute.

As for the fourth possibility, it's drawn from the realm of the occult. There are demonic entities known as egregores which are created and nourished by human energies. They are distinguished from the true demonic hierarchies in that their existence is mental rather than spiritual. An egregore is like a delusion that's somehow become real; a powerful egregore such as liberalism is a mass delusion. The more people enslaved to it, the more mental energy it feeds on, and the stronger and more real it becomes.