OBOR is a Chinese project designed to maximise Chinese interests and benefits.
It is not a hand out to the world.
The goal of OBOR is to vastly improve Chinese land connections first to central Asia, then the Middle East and eventually onwards to Europe and Africa.
With Europe as the eventual destination, detouring South to India makes little sense, especially in the initial launch stage we are seeing now.
Branching out to link OBOR to tangential (to the direction the route wants to go) economies is a secondary objective, that will probably only become truly attractive once the core links to the ME, Europe and beyond are well established as countries seek to top into this new opportunity.
By and large, I think the emphasis falls on these tangential economies (which India is one) to approach China to ask to link themselves to China's OBOR project to benefit from all the work China is doing. Because making those links will benefit those economies far more than it would China.
Given its size and importance, obviously India won't need to come cap in hand to Beijing to ask for permission to join, but OTOH, if India is expecting China to come to Delhi cap in hand to beg India to join, they will be disappointed.
The bottom line is that India just isn't as important to China as most Indians would like to think. It gets the respect and attention its size (economic) and power (political and diplomatic) demands in Beijing, no more, no less.
In terms of economics and strategic considerations, India's limited economic integration with China means its not a high priority for the Chinese government when planning for the OBOR, and the infamous red tape and thinly veiled political hostility in Indian towards everything Chinese would also be massive factors acting against India being seem as core component material for the Chinese OBOR.
So to sum up, China is expecting friendly and highly motivated countries to be lining up to get a piece of its OBOR pie, most of whose inclusion in the project would directly further China's ultimate plans and goals for OBOR.
In that context, India, who is of underwhelming importance to China, whose geographical location means its inclusion would not be directly helping to advance China's immediate or ultimate plans for OBOR, and who's toxic investment and political climate towards Chinese involvement within India all contribute to India being seen as a marginal piece within the context of OBOR's initial stages.
India's inclusion would obviously be beneficial to all, but its exclusion would hardly make Chinese leaders loose sleep over.
..realistically India and China have a lot of work to do vis a vis their bilateral relationship. India has certain geopolitical considerations that China needs to be cognizant of ( and respect!) And the the vexed border issue. That's why I refer to what I did in my previous post I.e. the element of economic coercion 
