One of the biggest mistakes you can make as a writer is to decide you don't need feedback.
No matter how long you've been writing or how great you think your work is, if you're the only person reading it prior to publication you're not putting your best work out into the world.
Other eyes will see mistakes you've never noticed- it's the difference between a group of people putting together a complicated puzzle and one person doing it alone.
Can the lone person put the puzzle together? Eventually and with a lot of struggle- yes. The group can do it faster as each individual will see aspects of the pieces the others missed.
The same is true of writing. You know what you meant when you put the words down on the page, you know the backstory of each character, you can see the location in your mind's eye.
When you're looking at the words on the page you're reading what's there. You're also "reading" what you think is there (because you remember it so clearly... even though you never wrote it down).
Your readers do not have that advantage. They can't read your mind, they're limited to the words which actually made it onto the page. If you're writing about the red rocks of Sedona and you fail to mention that they're cliffs, your reader might think of lava rocks littering their front yard.
Receiving feedback gives you the opportunity to fix mistakes before you send your work out into the cold, dark, sometimes uncaring world. It can make all the difference between getting an acceptance versus getting a rejection.
Giving feedback is possibly more useful when it comes to growing as a writer. Looking at someone else's work can inspire you. Their work might provide the springboard toward new ideas you may never have come up with on your own.
Aside from the boost to the imagination, reading someone else's work can help you parse different ways of describing the world in which your work resides.
Look at these examples of different authors describing Los Angeles:
"Los Angeles is 72 suburbs in search of a city.” -Dorothy Parker
“A good part of any day in Los Angeles is spent driving, alone, through streets devoid of meaning to the driver, which is one reason the place exhilarates some people, and floods others with an amorphous unease.” -Joan Didion, "After Henry"
“Koreatown was an L.A. neighborhood that told the city’s entire history through its architecture — from 1920s apartment buildings with art deco iron lettering on top of the roofs to the neon, layered storefronts that arrived loudly in Los Angeles via Seoul.” -Maurene Goo, “The Way You Make Me Feel”
“You can’t tell a story about L.A. that doesn’t turn around in the middle or get lost.” -Eve Babitz
From those quotes you get several ideas of what Los Angeles is like.
Los Angeles is fragmented and searching for it's identity.
Los Angeles is lonliness.
Los Angeles is confusing.
Los Angeles is full of history.
None of those descriptions rely on describing the actual place- there's no "take the 8 to the 5 and you'll see giant palm trees." However, they each evoke a sense of place that speaks to the themes they tackle in their work.
Reading those works can inspire how you write a description of your world, beyond simply describing what we "see" when we read.
Giving feedback also allows you to help another writer through road blocks in their own work that can help you recognize road blocks in your own.
Say the other writer is stuck in the middle of their book because they don't know how the characters get off the mountain and save the little Christmas village. You might suggest they make snowshoes or a sled out of branches to get down the mountain more quickly.
Applying your logic and brain power to their issue allows your brain to continue working on plot issues in your own work on a subconcious level. You may find yourself suddenly having an "ah ha" moment where you figure out how to solve the problems in your own work.
It can also help you highlight a bigger issue with their work which they haven't noticed.
During one manuscript swap I had to give the awkward feedback that their mystery novel did not, in fact, contain a mystery. If they'd submitted the work as a liteartuer endeavor, it might have worked but barely. They'd spent over a year working on the novel and imagining it as this great heist mystery, without realizing they'd scrubbed everything from the book which contained the actual mystery.
My feedback helped them retool their novel so they can send it out for a manuscript swap again. (They also helped me realize how much I rely on the word "so" in my writing. A habit I am desperately trying to break but haven't yet managed to do so.)
The final reason giving and receiving feedback is important is in building relationships with other writers. There is little in this world which is more vulnerable than sharing your writing- its as though you're laying your soul bare for the world to see. Allowing someone to see your work before it's finished takes bravery.
Reciving feedback takes a level of trust that they have your best interests at heart.
Giving feedback shows you have their best interests in the forefront of your mind.
Giving and receiving feedback is a useful tool for all the reasons above. I urge you to put your work out into the world to get that feedback before you start submitting it to agents or magazines (etc.). It can only make you a better writer.