How did pirates back in the day not get killed themselves when they attacked ships?

The Somali pirates operate very much the same as pirates in the past. They use fast small ships and light weapons. Their most important weapon is fear. God help you if you resist, or try to resist!

1- Commercial vessels were not well armed

A gun is a very heavy object that lessens profit. Each gun weighs at least half a ton. Add to that ammunition and gun crew. Make it a ton altogether. A commercial ship is not a man of war. If it is equipped with 20 guns, it can carry 20 ton less cargo. Ships would carry as few guns as possible.

2- Pirate ships were small and fast

Pirates would operate small, fast ships, like sloops or schooners. They could be maintained anywhere. That's important, because they couldn't simply sail into a port and have it serviced there. A fast ship could outmanoeuvre any commercial ship. That's far more important than being large and impressive. Once a ship spotted a pirate, it had very little chance to escape. Unless it was close to port, or a warship was nearby.

3- Pirates were ruthless

What you never see in pirate movies is what pirates would do to anyone even attempting to resist. You'd be tortured in the most horrible way possible to death. Not just 'walking the plank', but in the most horrible way imaginable. Think: gauging out eyeballs, and having the victims eat them. That sort of thing.

That was simply good economics: anyone surrendering immediately had a chance on survival. Anyone remotely resisting, that might even be a dirty look, would be tortured to death. The result was that most merchantmen immediately surrendered without a fight.

That's not something Hollywood likes to show. Pirates were not "gentlemen of the sea". They were the absolute scum of the earth. Most people would barf if they knew what pirates would do to their victims.

• https://www.ranker.com/list/ways-pirates-killed/nathan-gibson
• https://www.pirateshowcancun.com/blog/jolly-pirate-speak/top-7-pirate-punishments-no-7-will-make-you-squirm/
• https://www.worldhistory.org/article/1847/pirate-punishments-in-the-golden-age-of-piracy/
• https://archive.archaeology.org/online/reviews/pirates/poll.html
• https://www.thevintagenews.com/2021/10/18/these-depraved-pirate-punishments-would-make-captain-jack-sparrow-shiver-his-timbers/?firefox=1
• https://listverse.com/2016/03/03/10-of-historys-most-terrifying-and-brutal-pirates/
• http://cindyvallar.com/torture.html

4- There was no pirate flag

Some pirates flew a flag, but it wasn't standard practise. Some did, most did not. They flew any flag that would bring them closer to their victim.

It's not like nowadays when nobody seems to care one bit about their work and just assume that "it will all be handled by insurance".

That's not correct. Ships were insured, most of them. Before the Golden age of Piracy, the Dutch VOC was formed in 1602, precisely for that reason. A single ship was too costly, and the risks were too high for one investor. Piracy was just one of the many risks. Most nations followed, sooner or later, by setting up stock exchanges, insurance and companies with stocks. Lloyds of London was formed in 1686. Many if not most commercial long distance ships were insured.

Those ships were far more likely to surrender immediately. "The insurance will pay anyway." Ships that weren't insured and owned by the captain, or the owner present on the ship, would loose everything. They were more likely to resist.

With that in mind, I cannot imagine that pirating would be very "jolly" for the pirates themselves.

No it wasn't. Conditions were pretty bad on board. Very cramped accommodations, bad food and a reasonable chance to get killed. Either by disease (most likely), or by combat, or later by hanging. Pirate ships were always small, but their captains tried to cram in as many crew as possible.

The upside was the pay and the more democratic working conditions. If a captain was successful, the pay was good. If not, no pay at all. Pirates usually elected their captain. An unsuccessful captain was swiftly replaced. If he was (very) lucky, by vote.

Perhaps I'm completely mistaken about the "average cargo ship" in those days? I imagine them being full of well-dressed soldiers

Absolutely not! An average merchant sailor wasn't uniformed. Some captains paid for that, most did not. There were no soldiers on board. Even the gun crews were civilians. Almost always (civilian) sailors with some extra training. Perhaps a retired navy man would be there, but normally merchant ships sailed without military crew.