Feudalism bites way more than you could ever imagine.
To understand what exactly the barons were griping about in the Magna Carta, you need to understand some of the lesser-known and most aggravating details about feudalism.
So at the top you have the monarch who literally owns everything. Think back to that scene in The Lion King where Simba is told that, "Someday everything the light touches will be yours." Yeah, back in the day, they really meant that.
The king technically owned all the land in the whole kingdom himself. But having it all isn't actually very convenient, so he would rent out chunks of his kingdom to his best friends and relatives (the nobility).
Noble families with fancy titles like duke, count, earl, and baron, would control whatever land the king granted to them and pay him back in taxes.
However, these taxes were basically nothing like what you're used to. These were absolutely not add-up-you're-income-and-dependents and mail a check by April 15. The king got to demand taxes for all kinds of things beyond just a yearly due. Traditionally, major life events like weddings, deaths, and career advancements were taxed.
Gives a whole new meaning to the phrase "death and taxes," doesn't it?
As if that weren't bad enough, taxes would go up anytime the king wanted to wage a war against somebody…which back then was pretty much always. English kings would basically raise an army to attack France the day after they were crowned; it was just what they did.
And in addition to paying more hard-earned sacks full of coins, the king would also tax his nobles in the form of soldiers. He would demand that they send him a certain number of knights, bowmen, and other weapon-wielding dudes ready to fight, die, and not ask too many questions about what this beef with France (or wherever) was really all about.
The nobles wouldn't have been able to pay all these taxes on their own; they spread the pain around, or at least downward.
Much like the king, nobles divided their lands into plots that could be rented out to vassals (called "free men" in the Magna Carta). Families would work for a noble paying him rent and taxes in all the same ways that the nobles paid the king. So that meant vassals paid their lord all those dumb special-occasion type taxes and had to provide dudes with sharp objects to their lord, for him to send to the king, every time the king wanted to look cool.
Working for these vassals were serfs—who weren't exactly slaves because they did get paid, but they also weren't free because they couldn't leave. These are the laborers who worked on the land for the vassals in exchange for a place to live and the medieval equivalent of minimum wage. They were stuck in a kind of permanent indebted state at the lowest rung of feudalism. And yes, the free families get to tax them for all the same stuff and call upon male serfs to grab a pitchfork or a large rock or whatever and march off to war too.
Okay, so this is the social hierarchy people were living in at the time of the Magna Carta, but it's not like feudalism was anything new. And the church was doing a pretty good job of telling people to just accept their fate and wait around until it's time to go to heaven.
What had changed was the fact that the royal family had started further abusing a system that was already built on a long tradition of abuse.
At the time of the Magna Carta England was ruled by the House of Plantagenet, a dynasty of kings who are not exactly remembered for being judicious statesmen.
King Henry II spent his reign (1154-1189) fighting wars with France, Ireland, and his own family, all of which cost a lot of money and required new taxes. His son, who became King Richard I, left England to go on Crusade and took oodles of cash with him leaving his brother John behind to squeeze money out of the increasingly annoyed populace.
When John finally was crowned king in 1199 he was already notorious for finding new and ingenious ways to tax people, a talent that he continued to employ. He basically dredged up all previously used (but forgotten) forms of taxation, raised their rates, and started demanding them as if people should have been paying them all along.
He was especially sleazy in his methods for taxing people he disliked and having people arrested and fined without a trial or any evidence of a crime. You can see how he might have been a bit disliked.
The final straw was probably the fact that England had a few bad harvests in the early 1200s. And, of course, their taxes weren't tied to how much money or food anyone had, so King John just went along asking for more money despite the fact that people had less to give.
The rebel barons who stood up to him weren't protesting against the whole feudalism system, just the out-of-control element at the top. The Magna Carta doesn't try to grant freedoms or justice universally—and certainly not to serfs—it just tried to establish some boundaries for evil Sir Tax-A-Lot and his newfangled ways of extortion.
Everything else they accomplished was just bonus.