Perhaps a good mental model comes from sales. Treat it as a sales funnel. Leads, qualified leads, meetings booked, follow up meetings (serious), term sheet. Or whatever. It's a numbers game, pure and simple. 500 leads (look up lots of VCs and see if they have invested in anything similar) leads to 80 qualified leads, leads to 50 calls, leads to 10 follow up calls, etc. If you think about it this way, every "rejection" is just a person in your funnel, and your funnel shows lots of people will fall out. Who gives a shit, just keep going.
Obviously it isn't the exact same thing as doing sales, but, who cares? Sales folks have been dealing with rejection since the beginning of time, and from the folks I know in sales, when they have prospects (ie people in the funnel) and they can just keep moving them along, they seem to be ok psychologically.
The key thing about sales is that it's about what the customer wants, not you. In addition, most investment pitches result in "no", so you need to get out of that expectation-path as quickly as possible. (Most pitch templates that you see on the web get one or both of these wrong.)
"Qualified leads" mentioned above is very important. "qualified" is far more than "I think that they have money". It's "they're investing money in companies like mine RIGHT NOW." (VC funds do all of the new-to-the-fund investments during the first 1-3 years of the fund. During the next 7+ years, they just make follow-on investments in the winners. If a VC firm has $400M and four partners, they don't have the time to do $100k investments. The investors that you want don't invest in competitors. And so on.)
The other thing is that you have to sell what they're buying, which is an investment with the kind of return that the investor is looking for.
"Investment" trips up a lot of people. A good product is not enough; there are lots of good products in bad businesses. A good business is not enough - there are many great businesses that are not venture-investable. (Amazon, Apple, and Google stopped being venture-investable long before they stopped being great businesses.) There are even great investments where the current product is pretty bad.
The "kind of return" is important. Venture investors are NOT interested in "100% chance of 3-5x in three years". (That might work for private-equity firms.)
Early stage VC firms want each investment to have "return the fund" potential. (Yes, the $400M fund mentioned above is looking for companies where their 20-25% for $4M can return $400M.) They're willing to accept "70% will return 0, 15% will break even, 10% will return <10x" risk to get that upside potential. Some angels have a different risk profile, but if you'll need VC investment later on, they'll use the VC criteria.
You also need to understand how the person you're pitching makes money. VCs and angel groups need exits within a reasonable period of time. (LPs insist on exits and someone in every angel group does as well.) Some individual angels don't.
Do not take "how to pitch" advice from people who haven't either raised money or made a reasonable number of investments. In fact, the latter are often a bit wrong about what gets them to invest.
BTW - Don't ask someone who says "no" for an introduction. The first question the introducee will ask is "did you invest?" (The exception is when Marc Andreessen calls a friend with a small fund and says "I can't do deals this small.")
Obviously it isn't the exact same thing as doing sales, but, who cares? Sales folks have been dealing with rejection since the beginning of time, and from the folks I know in sales, when they have prospects (ie people in the funnel) and they can just keep moving them along, they seem to be ok psychologically.