Why can't I define inline functions inside Angular templates ? How else to do it?

This works fine if you just provide the expression you want Angular to evaluate. If you have a property on your component e.g. value, you can just use the following:

<button class="btn btn-primary" (click)="value = 'hi'">
    Click Me
</button>

Angular essentially just calls the code that you provide as if it were inside a function (that's a big simplification, but works for your purposes).