Edit in JSFiddle

$('#btn-center').click(function(event) {
	 var outerContent = $('.cat-container');
   var innerContent = $('.cat-container > ul');
   outerContent.animate({scrollLeft:(innerContent.width() - outerContent.width())/2}, 500)
});

$('#btn-center-element').click(function(event) {
	 var middleElement = Math.round($('.cat-container ul li').length / 2);
   var outerContent  = $('.cat-container');
   var innerContent  = $('.cat-container > ul');
   var targetElement = innerContent.children('li').eq(middleElement -1);
   
   targetElement.css('border', 'solid 2px red');
   outerContent.animate({scrollLeft:  (getTotalWidth(middleElement -1) - 20) }, 500);  
});

$('#btn-element').click(function(event) {
	var input        = $(this).prev('input').val();
  var catCount     = $('.cat-container ul li').length;
  var innerContent = $('.cat-container > ul');
  var outerContent = $('.cat-container');
  
  if(input && input > 0 && input <= catCount) {
  	var targetElement = innerContent.children('li').eq(input -1);
    targetElement.css('border', 'solid 2px red');
    outerContent.animate({scrollLeft: (getTotalWidth(input -1) - 20)}, 500);
  }
  else {
  	alert('Please enter a valid number in')
  }
});

$('#btn-reset').click(function(event) {
	var outerContent = $('.cat-container');
  var liElements = $('.cat-container > ul li');
  $.each(liElements, function() {
  	$(this).css('border', 'solid 2px orange');
	});
  outerContent.animate({scrollLeft: 0}, 500);
});

function getTotalWidth(number) {
	 var liElements = $('.cat-container > ul li').slice(0,number);
   var total = 0;
   $.each(liElements, function() {
   	total += $(this).width();
   });
   return total;
}

<div class="main">
  <h1>Cool Cats</h1>
  <div class="cat-container">
    <ul>
      <li>
        <a href="http://thecatapi.com"><img src="http://thecatapi.com/api/images/get?format=src&type=gif"></a>
        <div class="cat-title">
          <h3>Cat 1</h3>
          <p>description</p>
        </div>
      </li>
      <li>
        <a href="http://thecatapi.com"><img src="http://thecatapi.com/api/images/get?format=src&type=gif"></a>
        <div class="cat-title">
          <h3>Cat 2</h3>
          <p>description</p>
        </div>
      </li>
      <li>
        <a href="http://thecatapi.com"><img src="http://thecatapi.com/api/images/get?format=src&type=gif"></a>
        <div class="cat-title">
          <h3>Cat 3</h3>
          <p>description</p>
        </div>
      </li>
      <li>
        <a href="http://thecatapi.com"><img src="http://thecatapi.com/api/images/get?format=src&type=gif"></a>
        <div class="cat-title">
          <h3>Cat 4</h3>
          <p>description</p>
        </div>
      </li>
      <li>
        <a href="http://thecatapi.com"><img src="http://thecatapi.com/api/images/get?format=src&type=gif"></a>
        <div class="cat-title">
          <h3>Cat 5</h3>
          <p>description</p>
        </div>
      </li>
      <li>
        <a href="http://thecatapi.com"><img src="http://thecatapi.com/api/images/get?format=src&type=gif"></a>
        <div class="cat-title">
          <h3>Cat 6</h3>
          <p>description</p>
        </div>
      </li>
      <li>
        <a href="http://thecatapi.com"><img src="http://thecatapi.com/api/images/get?format=src&type=gif"></a>
        <div class="cat-title">
          <h3>Cat 7</h3>
          <p>description</p>
        </div>
      </li>
    </ul>
  </div>
  <div class="button-container">
    <button id="btn-reset"><span>Reset</span></button>
    <button id="btn-center"><span>Center-Size</span></button>
    <button id="btn-center-element"><span>Center-Element</span></button>
    <div class="input-button-container">
      <label for="element-num">Pick a Cat item number to center on:</label>
      <input type='text' name="element-num" id="" />
      <button id="btn-element"><span>Selected-Element</span></button>
    </div>
  </div>
</div>

div.main {
  display: flex;
  flex-direction: column;
  align-items: center;
  width: 100%;
}

h1 {
  display: block;
  color: white;
  background-color: orange;
  width: 100%;
  text-align: center;
}

div.cat-container {
  overflow-x: scroll;
  overflow-y: hidden;
  height: 250px;
  width: 400px;
}

div.cat-container ul {
  width: 1000px;
  padding: 0;
}

div.cat-container ul li {
  float: left;
  margin-right: 20px;
  list-style: none;
  border: solid 2px orange;
  padding: 5px;
}

div.cat-container ul li a {
  display: inline;
}

div.cat-container ul li a img {
  height: 100px;
  width: 100px;
}

div.cat-title {
  margin-top: -15px;
  text-align: center;
}

div.cat-title h3 {
  background-color: orange;
  color: white;
  width: 110%;
  text-align: center;
  position: relative;
  left: -5px;
}

.button-container button {
  font-weight: bold;
  color: white;
  background-color: orange;
  display: block;
  margin-top: 20px;
  outline: none;
  cursor: pointer;
  text-align: center;
  text-decoration: none;
  padding: .5em 2em .55em;
  text-shadow: 0 1px 1px rgba(0, 0, 0, .3);
  -webkit-border-radius: .5em;
  -moz-border-radius: .5em;
  border-radius: .5em;
  -webkit-box-shadow: 0 1px 2px rgba(0, 0, 0, .2);
  -moz-box-shadow: 0 1px 2px rgba(0, 0, 0, .2);
  box-shadow: 0 1px 2px rgba(0, 0, 0, .2);
}
.button-container button:hover {
  backgound-color: red;
}
.input-button-container {
  margin: 20px 0;
}
.input-button-container label{
  display:block;
}
.input-button-container button{
  display:inline;
  margin-top: 15px;
}
.input-button-container input{
  height: 30px;
  width: 35px;
  display:inline;
  text-align:center;
}