Why webkit line clamping does not work in firefox?

Important Update:

As of Firefox version 68 Firefox supports -webkit-line-clamp!!

Demo snippet (caniuse)

p {
  width: 300px;
  border: 2px solid green;
  padding: 0.5em 0.5em 0 0.5em;
  overflow: hidden;
  text-overflow: ellipsis;
  display: -webkit-box;
  -webkit-box-orient: vertical;
  -webkit-line-clamp: 3; /* number of lines to show */
}

<p>When the CSS -webkit-line-clamp property is applied to a block of text (e.g., a paragraph), the text is limited to the specified number of lines (1 or more), and an ellipsis character (…) is added to the end of the last visible line. - see <a href="https://webplatform.news/issues/2019-05-17">webplatform.news</a>

Although Firefox uses the Gecko rendering Engine which uses the -moz- vendor prefix, since version 49, Firefox decided to add support for several -webkit- prefixes and WebKit-specific interfaces

Note: CSS Overflow Module Level 3 Editor's draft includes an official property line-clamp - which will likely replace the proprietary-webkit-line-clamp property.

Original Answer

You can't. -webkit-line-clamp is for browsers that use webkit. Firefox runs on gecko and uses the vendor prefix: -moz-

If you're interested - you could take a look at my answer here: a line-clamp with fade-out fallback fiddle which adds a fade-out effect workaround (instead of ellipsis) for non-webkit browsers.

/----line clamp---/

.line-clamp {
    position: relative;
    height: 2.7em; 
    overflow: hidden;
}
.line-clamp:after {
    background: $white;
    bottom: 0;
    position: absolute;
    right: 0;
    float: right;
    content: '\2026';
    margin-left: -3rem;
    width: 1rem;
}

@supports (-webkit-line-clamp: 2) {
    .line-clamp {
        display: -webkit-box;
        -webkit-line-clamp: 2;
        / autoprefixer: off /
        -webkit-box-orient: vertical; 
        / autoprefixer: on /
        max-height:3.6em; 
        height: auto;
    }
    .line-clamp:after {
        display: none;
    }
}

/----line clamp end---/