Firstly, let's check the meaning of sceptical
Sceptical means: a person that is not easily convince

We all know that "seeing is believing".
No man would want to invest his income on what he is not sure of.
So, while trying to convince someone to buy bitcoin, you must do the following

1)Show the evidence of your own benefit(profit) from bitcoin (i.e - every man would want to invest on something attached with profit)

2)Explain the process in details

3)Assure the person that bitcoin is safe (because no man would want to lose his money)

4)Promise to share regular info regarding every activities of bitcoin

You really don't need to convince anyone to accept bitcoin but if you want to go down that lane then you might consider adding the following: Bitcoin transactions are fast and secure, and can be done without the need for a middleman or intermediary, which can save you time and money in transaction fees. Additionally, Bitcoin is a decentralized currency, which means that it is not subject to the control of any government or financial institution. This makes it a safe-haven asset in times of economic uncertainty or inflation. Furthermore, Bitcoin is a scarce asset, with a limited supply of 21 million coins, which makes it an attractive option for those looking for a store of value or long-term investment.

Bitcoin isn’t a new product on the shelf we have advertise. To add to what’s already been said, convincing people to invest in bitcoin is a slippery slope, if the person trust you and is convinced to buy bitcoin, you put yourself in a position where you’re now the center of the investment. Bear in mind they will on your neck if there is any problem be it a bearish market or godforbid they lose their private keys, I don’t like to tie myself to other people’s money or give financial advice.

First, educate them, if someone showed interest it's a good sign to convince them, it's important to educate skeptical individuals about the benefits and risks of Bitcoin so that they can make an informed decision.  Because if you insist, it might someday when they will fail they will surely blame you in the future.

Let them decide on their own, at least they know already the pros and cons of Bitcoin investment.
Because these kinds of people are usually wasting time because they have an attitude of not easily believing.  Because when dealing with a skeptical person, it's important to listen to their concerns and address them with accurate information.  Be patient and understanding, and avoid being overly pushy or aggressive in trying to convince them.  Respect their decision and not pressure them into investing in something they're not comfortable with.

I am going to go a bit against it and say why bother.
There are people on the edge that you can 'push over' and have them get into BTC
There are people who may or may not be interested in BTC and need to get more knowledge info that you can convince to invest in and use BTC.

But someone who is skeptical? May not be worth the time & effort.

Just my view.

-Dave

Aside from the fact that you can safely and easily self-custody Bitcoin, it is decentralized. That is the most convincing feature of Bitcoin. It doesn't have the abusive rulers who got all the powers in their hands as far as money is concerned. Bitcoin is ruled by codes that are etched in stone, that can't easily be tweaked in whichever direction the greedy fiat gods think of. The same decentralized feature means it doesn't have a CEO or a president to kill, a headquarters to raid or burn, central server to seize, and so on and so forth, which government agencies are fond of doing to anything in their way.

But if a skeptical person isn't convinced of this, try telling him/her the real situation of fiat and banks and governments and how ludicrous the monetary system actually is. If he/she is still skeptical, it might help mentioning to him/her that the likes of Elon Musk, Ray Dalio, Tim Draper, Jack Dorsey, Robert Kiyosaki, Tim Cook, and many others also own Bitcoin. If he/she isn't convinced of Bitcoin, perhaps these influential personalities, one of which he/she might idolize, have found something.

From the beginning until now, there are many people who are skeptical of bitcoin, but the fact is that until now the number of people interested in investing in BTC, in my opinion, has not decreased. In fact, I think that one day the number of people investing in Bitcoin will definitely increase.

so I don't think there is a need to convince people in a hurry because later they will look for it themselves.

Some of you guys like to talk about the investment side to convince others, with a speech like: bitcoin is good to invest in.
But you're having a misconception about the purpose to create Bitcoin.

The currency hasn't be created to make you "rich" overnight. It was not launched as a quick rich scheme, and for exemple I challenge you to find me a single post from Satoshi saying something like: buy bitcoin! you will be rich!

Investing in Bitcoin and make money.
I can do the same with the traditionnal currencies. I can trade USD, EUR, CHF, GBP... and also make money.
So what?

Huge profits you may argue.
There are traditionnal assets performing higher than Bitcoin.
So what?

No 3rd parties to store your money.
I can do that with gold as well.
So what?

Safe haven.
Seriously? Ask to people who bought BTC at $60,000 what they think about it.
The Swiss franc, bonds, or gold, yes, but Bitcoin?
Even investing in a safe haven may be not a good choice when the stock markets are rising

What about to use Bitcoin for what it was supposed to be? A payment mean and an alternative currency? Hence the name Altcoin.
You should rather use this argument if you want to convince someone, and if the person is not convinced, it's perhaps because he has no needs

I won't do that, there's no reason for me to force or beg someone to invest in bitcoin, it's not in my favor, and they'll even blame me if they lose. You shouldn't try to give someone advice to buy something they don't like, it's not a good idea.

I know you mean to help people because bitcoin really is a once in a lifetime opportunity, if we miss it, we will have to wait a long time for another chance. But people won't think so, what they think is that you are trying to scam them. If they are passionate about bitcoin, instead of explaining it to them, give them the necessary materials to study on their own.