First, some support for the question since some people are questioning the premises, then an answer.

Support for the premises of the question

This is empirically documented in Pankaj Ghemawat's "World 3.0"

World 3.0: Global Prosperity and How to Achieve It: Pankaj Ghemawat: 9781422138649: Amazon.com: Books

Here is a relevant graph from the book (I think this qualifies as fair use...):

To interpret this, note that there is a clear correlation between perceived need for cultural protection and (self) perceived cultural superiority. So people who think their cultures are superior to the rest of the world are more likely to believe that it needs protection from external "corruption."

India is at the very top right (the size of the circles represent population, so that other big one is China). Ghemawat interprets this (correctly) as insecurity. Countries like Sweden, Great Britain, France and Germany -- all countries with plenty to be proud about and easy/obvious cases for believing in their own superiority, actually bring up the rear of the distribution.

The US is somewhere in the middle. Japan is a bit further up. Among the BRIC countries, India is the outlier (Brazil, Russia and China all are in the middle). For company at the top of the distribution, India has Tanzania, Ethiopia, Indonesia, Pakistan, Turkey, Bangladesh, Turkey...see a pattern here?

This is what BJP style thin-skinned jingoism looks like statistically (and its equivalents in similar countries, though none is as extreme as India).

This is not an answer to the question but support for the question being a sound and well-posed one. Your instincts are correct.

The answer

Now as to why, the zeroth-order answer should be obvious, if useless. Indians pretend to be proud because they are so uncomfortable (insecure rather) about their core identity. Effect and cause.

It is a defense mechanism that would be unnecessary if the case for being proud were actually as brain-dead obvious as it is with the countries at the back of the distribution.

So the second order question is, why are they insecure?

Two reasons:

First, objectively, Indian culture today, taken on an average, has much less to be proud relative to other countries (not even accounting for size) and even relative to itself for much of its history. The objective situation is improving but very slowly. Take away the things we usually brag about: the space program and Tendulkar, Anand and the IITs, and what you have is... everything else, and it isn't that pretty.

Second, it is easier to cherry pick and weave a narrative around things to be proud about and go into denial about everything else rather than do something about things that are not sources of pride. Basic confirmation bias operating on national grand narrative. This is understandable. It sucks to reflect on the true state of affairs. It is comforting to focus on the positive. It is even justifiable to some extent, since it can create energy for action. But when the underlying narrative is seriously deluded, it is not a solid foundation for action.

For a lot of Indians this cherry picking translates to flogging the dead "we invented the decimal system" horse (even granting that case, which is not as clear cut as Indians like to believe, what have we done for the world lately?) coupled with a few modern highlights like having a space program, an IT industry, a chess grandmaster and a few Nobels. For dessert, if we still haven't fooled ourselves, there are plenty of others to blame, ranging from Islam to the British Raj.

We'd rather not talk about (for instance) the first thing that assaults foreigners when entering the country -- the lack of basic sanitation. We'd rather brag about the GSLV and nukes than talk about the good work being done by Sulabh Shauchalaya which we hope nobody notices is so necessary. In my opinion, Sulabh is the single most important organization in India, as far as the country's collective psychological health is concerned, not just in sanitation.

When clumsy foreigners or blunt NRIs like V. S. Naipaul point out the obvious, they are attacked. For the record, I've been an NRI for 15 years now, but I've felt exactly this way all my life. I can just articulate the arguments better today.

The only solid solution to this problem is to stop focusing on the high watermark achievements (nukes, space, Vishwanathan Anand, Tendulkar) and "raise the floor" so to speak. This means anchoring our sense of collective pride to the baseline least-common denominator standard of living (toilets, nutrition, safety for women, clean water, true exorcising of the demon of caste -- we're sort of in a Jim Crow phase as far as dealing with caste goes).

You manage what you measure. Genuine pride measures the things it is anchored to. When pride is linked to availability of toilets, toilets improve. When pride is linked to the ability to nuke Pakistan or China, those capabilities improve. For a long time, we've anchored pride to exactly the wrong things. Anchoring pride to winning Olympic medals is somewhere in between focusing on the top versus focusing on the bottom. A strong sports culture -- a middle-level concern -- leads to Olympic medals as topline signs, and a healthier population as a bottomline sign.

Swedes aren't secure in their identity because they win Nobel prizes (which they award themselves far less than you'd think) or build high-tech things (they do). They are secure in their identity because even the poorest and least talented Swede can expect a good life and the richest, most talented ones don't grudge them their standard of living as "unearned" or "undeserved" the way capitalists do in the US and India.

This is not an argument for state socialism of the Swedish variety. It is perfectly fine to attempt to get there in other ways (through entrepreneurship or whatever). It is perfectly fine to end up with unequal societies and launch moon rockets. So long as there is continued attention to raising the floor continuously.

Raising the high watermark is false pride. It is easy to do exceptional things on an exceptional basis. Raising the floor is the real thing. That's what makes it possible to do exceptional things on a predictable basis. That's what countries at the bottom of the distribution do well. Most Swedes are extremely fit and sportsy, so the country predictably wins a lot more Olympic medals.

The important lesson to take away from countries like Sweden is that social identity and pride is NOT based on your greatest achievements. It is based on the things you are least proud of. The dark stuff. The stuff you like to sweep under the carpet. The stuff you put in closets when visitors show up at your home. Which in general translates to "how a society treats its least fortunate members."

It doesn't matter how good Ratan Tata, Narayan Murthy, the ISRO chief or Rahul Gandhi feel about themselves. So long as they can look out of their car windows once they leave their gated complexes and see somebody whose life is that of a human piece of trash, none of them can feel secure and proud in their social identity as Indians.

Countries need to learn this lesson in direct proportion to their position on the graph I opened with. India, empirically, needs to learn this lesson the most.