Starting with an unofficial definition:
To be beaten by life: Suffering so many bad experiences that you give up trying to struggle for a better life.
Here're a few more examples:
- Worn out, exhausted, and beaten by life, the homeless man lay down in the snow and accepted his fate
- I've never seen someone so melancholy, so beaten by life, to stay in bed when their friends are knocking at their door
- I feel beaten by life, I've thrown in the towel and will accept whatever happens to me.
"Throw in the towel" is another idiom. When boxers are losing a match and have no hope of winning, their coaches will throw a towel into the ring to stop the match and accept defeat on behalf of their boxers.
It can be used as an exaggeration, you might not feel bad enough to be truly beaten by life, but you might say it in a cheerful way during a conversation:
"How are you John?"
"Poor, downtrodden, and beaten by life. But otherwise I'm pretty good! How are you?"
Here it's used ironically, John isn't unhappy enough for his friend to be worried. He might feel a little bit tired and annoyed at his job, so he'll say he's "beaten by life".
As with "go your own way," march to the beat of your own drum has positive and negative connotations simultaneously. The connotations of each phrase are different, though. No simple, abstract description can fully convey the connotations of either phrase. To understand them, you must follow some of the cultural landmarks that echo in people's minds when they hear each phrase.
Thoreau
First, here is the passage from Walden, by Henry David Thoreau, which is usually considered the origin of the expression:
Why should we be in such desperate haste to succeed, and in such desperate enterprises? If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. It is not important that he should mature as soon as an apple tree or an oak.
The phrase refers to people marching in formation, their steps synchronized by a drummer whom they all hear. Now imagine that one man is out of step with the rest of the formation—he isn't "keeping pace".
The "formation" that Thoreau is referring to is the common, conventional practice of seeking money, physical comforts, and the respect of most people—which is how most people live. But some people don't care very much about conventional success. Some people feel called to unusual pursuits that most people don't respect and that don't pay much money, like joining the circus or the life of a hobo. These people are "marching to the beat of a different drum" than the "drum" that guides ordinary people.
Weirdness, Quirkiness
So, saying that someone marches to the beat of a different drum suggests that they are weird, maybe somewhat goofy, certainly idiosyncratic. It suggests that they probably will not "succeed" by conventional criteria of wealth and public respect (though in rare cases they might become extremely wealthy).
Just as with "Go Your Own Way" (1977), there is a well-known pop song called "Different Drum" (1967)—and the words are, again, those of a person rejecting a boyfriend/girlfriend because they think their lives need to follow different paths. In "Different Drum", the girl mainly needs to maintain her freedom and independence, which would be lost if she stayed with a boyfriend who adores her too much. The rejection in "Go Your Own Way" has a more conventional reason: "You don't care about me enough. So, you will have to do without me, i.e. go your own way."
A description, not a prescription
Another difference between the two phrases is that it makes more sense to say that a person marches to the beat of a different drum, than to tell a person to march to the beat of a different drum. Quirky, unconventional people are not that way by choice. The phrase explains their odd behavior: they march differently because they hear a different drum than the one that most people hear. It doesn't make sense to tell an ordinary person to march to the beat of a different drum. Ordinary people hear the same drum that most people hear. They don't hear the "far away" drum that quirky people hear.
"Go your own way" suggests self-reliance more than it suggests quirkiness. The Frank Sinatra song "I Did It My Way" suggests that even though he chose the hard, individualist path, he still succeeded by the usual standards of wealth and respect—more than most people, perhaps. "Go your own way" makes more sense as advice—and it can even serve as a contemptuous dismissal.
Best Answer
Laugh all you like, it's water off a duck's back to me.
You can criticise and ridicule me all day, it's just like water off a duck's back to me.
There are plenty more examples out there I'm sure but sufficed to say, you can use it whenever you wish to inform somebody that you are or were in no way bothered about what they said or did.