Why do people pretend or show off?

There is an inverse to what you are asking, there are some who show off their progress.

So, instead of showing off with a new phone or nice cloth they show off with their poverty, their ability to forbare, etc... in short, they show-off their progress.

Only because you tagged this in philosophy I will give you an example from Western Philosophy, but the truth is just the same.

Socrates gently mocking Antisthenes for a kind of inverse snobbery: taking too much pride in his austerity.

... when Antisthenes turned his cloak so that the tear in it became visible, Socrates said: “I see your vanity through the tear in your cloak.”

Sexual lust. Most beings want to be loved; want to receive attention; do not want to be and feel alone. Women (plus Cultural Marxist boys/men) are known to be vulnerable to political correctness & obedient conformity. It is easy for Corporate advertising to socially engineer women because women often struggle to deal with criticism & rejection (where as men are used to being criticized, rejected & trashed).

The Blessed One said: “A woman attends inwardly to her feminine faculties, her feminine gestures, her feminine manners, feminine poise, feminine desires, feminine voice, feminine charms. She is excited by that, delighted by that. Being excited & delighted by that, she attends outwardly to masculine faculties, masculine gestures, masculine manners, masculine poise, masculine desires, masculine voices, masculine charms. She is excited by that, delighted by that. Being excited & delighted by that, she wants to be bonded to what is outside her, wants whatever pleasure & happiness that arise based on that bond. Delighting, caught up in her femininity, a woman goes into bondage with reference to men. This is how a woman does not transcend her femininity.

AN 7.51

Why do people pretend? Or show off

The cause is something called "Asmi-māna", meaning "I-am-conceit". It's one of the 10 fetters (samyojanas) that bind a being to Samsara.

As seen in the illustration below, this fetter is only done away with at the attainment of Arahantship meaning that unless one is an arahant one has this fetter of conceit.

Puthujjanas love 2 things

• sensuality
• being told that they are good people, precisely for craving sensuality. If nobody tells them they are virtuous for craving sensuality, they build a little story in their head where they are good people for craving sensuality.

puthujjanas who crave sensuality will tell other puthujjanas who have good items and fame that they are good people. Everybody wins, according to those people.

It gets even worse. The western humanists even say that envy of wealth will make people compete, for jobs for instance, and by making people compete, they will produce and buy good quality goods and services but for cheap, as long as the people who run their republic will break monopolies. Those people call this progress.

When those people want to feel compassionate, they will mix their cravings for sensuality with some social fight they found. For instance, they love to organize concerts where they will listen to songs for several hours, exactly like when they want to be purely entertained, but in order to feel righteous (and not selfish like when they feel when they get entertained), they say that they organize this entertainment not be entertained but to ''make society aware of'', or ''in the name of'', or ''denounce'' some situation that they call ''unfair'' like some misery of some people living far away from them (like in third world countries). This is the best life for puthujjanas: they get all the entertainment they crave and they feel like good people making a change in society, when all they do is listening to music then going back home...

Puthujjanas who break the 5 precepts do exactly the same thing.