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<select
         class="cursoruser-pointer p-2 w-full rounded-full ">
    <option class="rounded-full "
            disabled selected value="">Language to learn</option>
    <option class="rounded-full">German</option>
    <option>Spanish</option>
    <option>English</option>
</select>

Shows

However if I add v-model = "selectedLanguage":

<select v-model = "selectedLanguage"
         class="cursoruser-pointer p-2 w-full rounded-full ">
    <option class="rounded-full "
            disabled selected value="">Language to learn</option>
    <option class="rounded-full">German</option>
    <option>Spanish</option>
    <option>English</option>
</select>

it stops showing the placeholder:

<script>
    ...

    export default {
        ...
        data: () => ({
                selectedLanguage: 'Language to Learn',
        }),
...

How do I fix it?

Answers

Your initial selectedLanguage value should be "" (empty string), since you specified the value of "Language to learn" option to be empty string (value=""). In addition to that, selected is not needed anymore since you are already using v-model

Demo: https://codesandbox.io/s/still-dawn-nu4m8?file=/src/App.vue