JSFiddle - React, Tailwind, and code Playground

HTML

<select name="month1" id="month1" size="1">
    <option value="0">January</option>
    <option value="1">February</option>
    <option value="2">March</option>
    <option value="3">April</option>
    <option value="4">May</option>
    <option value="5">June</option>
    <option value="6">July</option>
    <option value="7">August</option>
    <option value="8">September</option>
    <option value="9">October</option>
    <option value="10">November</option>
    <option value="11">December</option>
</select>

JavaScript

$('#month1').on('change', function() {
    var today = new Date();
    var birthdate = new Date();
    birthdate.setMonth($('#month1').val());

    var monthsToGo = (today.getMonth() <= birthdate.getMonth())
        ? birthdate.getMonth() - today.getMonth()
        : (12 - today.getMonth()) + birthdate.getMonth()
    ;
    alert(monthsToGo);
});