Which, well, isn't true.
It is true that backstory can be misused (and it can kill when used poorly), but it's much like any writer tool out there—it has to be done properly, with purpose, and in moderation.
In fact, I will go out on a limb here and say that there is a problem with your book if you have absolutely zero backstory. Why? Because backstory builds the foundation of the current story, of the characters who are part of it. Your story, if it emulates reality, does not happen in a vacuum. If a reader knows nothing of the character and their life pre-story, it's much harder to care about the things happening to them in the story.
Backstory—it's your bread and butter when it comes to characterization. And pitch perfect characterization? Essential to a compelling read.
The Right Form
Backstory isn't just flashbacks, right? There are many ways to get that info out—dialogue, action, memories, etc. It's important to use the entire arsenal, not just one trick. Look for ways to vary your backstory and make it work. It's totally possible.
The Right Balance
Like most things in writing, backstory can go wrong fast. Many would say the most common issue is having too much, but too much isn't the huge problem some make it out to be. You would be surprised how much backstory a book can handle when done right.
Example: The Hunger Games. In the second chapter, there is a six-page flashback. Yes, six whole pages of FLASHBACK. Collins stopped her tension-packed novel for six pages to tell us something about the past.
Was that a bad move? Oh, no. Not at all. It was the perfect move. The flashback I'm referring to is the one in which we learn the relationship between Katniss and Peeta, how him giving her that bread saved her family, how she has always felt indebted to him, and now she must enter the games with this person.
This flashback is the foundation for everything the reader feels about Katniss and Peeta through the rest of the novel. Would we have felt so strongly if we didn't know this about them? I'm gonna say no, probably not.
This flashback, while it seems counterintuitive, doesn't stop the forward action, it makes it mean something. It increases the tension. The book would not be the same without it.
The Right Placement
For me, placing backstory is the make or break, and it's often where writers make missteps. You can certainly have a six-page flashback, but it only works if it's relevant. In fact, backstory ONLY works when it's immediately relevant to your story.
Going back to The Hunger Games flashback, notice that it's placed at the exact moment it becomes important to the story—when Peeta is announced as the male tribute. There is no mention of it before that. No need. If that flashback came out of nowhere at the beginning? Though essential information to the book, maybe it would not be received as well because the reader would not have seen the connection immediately.
The Right Information
While backstory builds character, it's important to build the right things. At times, we can make the mistake of putting in the wrong bit of information. Does the reader need to know that your character never learned to ride a bike? If so, the reader will get on board with backstory about why. If not, the reader will be annoyed with backstory about why. It's that simple.
Basically, backstory has to feel essential to a reader. You get that and you're golden, no matter how much you put in (See If I Stay by Gayle Forman for another amazing use of flashbacks. Basically, over half the book is flashback and it ROCKS.). So don't feel like you have to chop out all your flashbacks and whatnot, just make sure they work. Don't avoid a tool because you can't use it—practice and study until you get it right, because it's a tool for a reason.