As a youngster I was terrified of public speaking, and could barely get words out. Now I have to give talks as part of my job from time to time (gave two last week, in fact), and I love it. I can't say exactly what changed besides my age, but I don't get nervous now at all. Its at least partly from practice, and partly from the realization that no one cares (or likely will even notice) if you make a mistake. I think what makes many people uncomfortable is that we live in a culture where modesty is valued, and it just doesn't fit most people's personality to command everyone's attention.
Some, notably from the field of evolutionary psychology, argue that fear of public speaking is an evolutionary adaptation. We've spent the bulk of our time (approximately 99%, but depending on your definitions) as hunter-gatherers living in small groups. Speaking something that was disapproved of may get you excluded from the group. A solitary human in ancestral times stood little chances of survival, let alone procreation. Thus one may argue, fear of public speaking is not only common, it is also natural. It is something we all have to overcome. I find comfort in this.
I think you're right. We live in a culture that, at the very least, is ambivalent about modesty. People are discouraged from tooting their own horn, or being too full of themselves; but pop culture is all about tooting, and we are expected to sell ourselves and pitch our ideas to employers.
I must say I do not think we live in a society that values modesty. sure being modest is encouraged and is viewed as a positive character trait, but I think we are experiencing a shift. I'll use Twitter as an example, Twitter as it is, is a site fueled by smugness and a sense of superiority. To be active on twitter you need to honestly believe that the possibly hundreds of people that follow you care about your inane thoughts and quips about the day. I realize e I am probably looking too much into this and by extension thinking that you care about what I have to say, And thats kind of funny in a way.
Still even though it is the internet you are still interacting with people that you know and see in real life. Of course you will not be as boastful as you would online but it is a good microcosm( can't really think of a better word) of social interaction.