Yes, the child component cannot delete itself. The reason is because the original data for rows is held in the parent component.
If the child component is allowed to delete itself, then there will be a mismatch between rows data on parent and the DOM view that got rendered.
Here is a simple jsFiddle for reference: https://jsfiddle.net/mani04/4kyzkgLu/
As you can see, there is a parent component that holds the data array, and child component that sends events via $emit to delete itself. The parent listens for delete event using v-on as follows:
<row-component
v-for="(row, index) in rows"
:row-data="row"
v-on:delete-row="deleteThisRow(index)">
</row-component>
The index property provided by v-for can be used to call the deleteThisRow method, when the delete-row event is received from the child component.