Do I not understand the flex-grow property?

Question

You have to specify a value for flex-basis as well (not specifying this property causes behaviour similar to using the initial value, auto).

Add flex-basis: 0; to both children or just set it with the shorthand:

.flex-item {
    flex: 1; /* flex-basis is 0 if omitted */
}
.big {
    flex-grow: 3;
}

http://codepen.io/anon/pen/JEcBa

Flex-grow is commonly misunderstood in this way. Flex-grow only controls how the left over space is distributed between flex items, not how big they are in proportion to each other.

What you're looking for is really just this:

.flex-item {
  width: 25%;
  list-style-type:none;
  border:1px solid black;
}
.big {
  width: 75%;
}

See also

• Flex-grow not working as expected (flex items don't have the widths I expect)
• In what circumstances is flex-shrink applied to flex elements and how does it work?

Authors are encouraged to control flexibility using the flex shorthand rather than with flex-grow directly, as the shorthand correctly resets any unspecified components to accommodate common uses.

https://drafts.csswg.org/css-flexbox/#propdef-flex-grow

.flex-item {
   flex: 1;
}
.big {
   flex: 3;
}

This is a working example

http://codepen.io/anon/pen/VjZYPV