Forward Index vs Inverted index Why?

The point that you're missing is that there is no real technical distinction between a forward index and an inverted index. "Forward" and "inverted" in this case are just descriptive terms to distinguish between:

• A list of words contained in a document.
• A list of documents containing a word.

The concept of an inverted index only makes sense if the concept of a regular (forward) index already exists. In the context of a search engine, a forward index would be the term vector; a list of terms contained within a particular document. The inverted index would be a list of documents containing a given term.

When you understand that the terms "forward" and "inverted" are really just relative terms used to describe the nature of the index you're talking about - and that really an index is just an index - your question doesn't really make sense any more.

Here's an explanation of inverted index, from Elasticsearch:

Elasticsearch uses a structure called an inverted index, which is designed to allow very fast full-text searches. An inverted index consists of a list of all the unique words that appear in any document, and for each word, a list of the documents in which it appears. https://www.elastic.co/guide/en/elasticsearch/guide/current/inverted-index.html

Inverted indexing is for fast full text search. Regular indexing is less efficient, because the engine looks through all entries for a term, but very fast with indexing!

You can say this:

• Forward index: fast indexing, less efficient query's
• Inverted index: fast query, slower indexing

But, it's always context related. If you compare it with MySQL: myisam has fast read, innodb has fast insert/update and slower read.

Read more here: https://www.found.no/foundation/indexing-for-beginners-part3/