I'm not being harsh, I'm trying to help :
Hi Diego Ferrari, my name is Nicolás Melian, I'm a web designer and developer.
By saying this, you lost half the interest before they even open the email, they can see that from the preview.
I found the website of your clinic looking for a dentist in Buenos Aires. Also I saw that you have more than 600 followers on Facebook. You are doing a great job.
Don't lick his ass, he doesn't need his ego boosted. He needs people he can trust and work with. And if he needs his ego boosted (maybe its cultural over there), he wants it to be about dentistry, not facebook followers. He is not a social media guy.
Although I do believe that the design of the website could be improved, that it is somewhat outdated and does not look good on mobile phones.
Talking shit about people's business doesn't make them notice a "pain point", it just make them not like you.
People spend hours with their cell phone, use it for everything and when they want a dentist they usually look for it in Google
He already knows that, and if he doesn't then he's not your customer.
I would like to help you with this! If you want to see my work I leave my portfolio:
https://nicomelian.com.
What you're doing here is you're putting the burden of the sale on the other person. You want him to do the work for you. He has to listen to you, check your portfolio, guess your prices, come up with ideas. When I get emails like this, even if I need the service, I don't respond. It just add works to my plate and ain't nobody got time for that.
Instead of trying to make him do the work for you, which shows you're not confident. Do the work for him. That means offer a real solution, a price bracket, a timeframe, and a reason why. Then you remove all the annoyance from dealing with you and it makes it super easy. For example :
Good evening Mr. Ferrari,
I couldn't visit your clinic when I was in Buenos Aires, so I'm contacting you here.
(the preview will show that, they will open it)
I specialise in designing and launching websites for the top dentists from buenos aires to whatever other town you worked with. I heard from a client you're one of the top dental surgeons in buenos aires, and so I thought we'd be a good match.
(ego boost, just like you like)
I actually already have an idea of a website in mind, modern look with an integrated booking system. That will make everything much simpler for your clients. It shouldn't take more than a week to launch and around $1000.
I wanted to send you more details, would it be better via email or via LinkedIn ?
<- so now you showed you're confident, that you work with the best, you boosted his ego in a way that he cares (about being a dentist), it sounds natural, its short, and you are not making him guess anything.
I wrote this in one go so don't hesitate to edit whatever. I hope it helps