How to make a delete request with Laravel

It's better to change your route to this mode:

Route::resource('tags','TagController');

You should register a resourceful route to the controller. This single route declaration creates multiple routes to handle a variety of RESTful actions on the Tag resource. Remember, since HTML forms can't make PUT, PATCH, or DELETE requests, you will need to add a hidden _method field to spoof these HTTP verbs.

<input type="hidden" name="_method" value="DELETE">

or add this in your form

{{method_field('DELETE')}}

You may try this (Notice the hidden _method input):

<form method="post" action="http://***/public/deleteTag/{{$tag->id}}"> 
    {!! Form::token() !!}
    <input type="hidden" name="_method" value="DELETE">
    <button type="submit">delete</button>
</form>

Check Form Method Spoofing.

Update:

In the latest versions of Laravel, it's possible to use blade directives for csrf and method in the form, for example:

<form method="post" action="..."> 
    @csrf
    @method('DELETE')
    <button type="submit">delete</button>
</form>