“Consumption lowers investment” mankiw explanation
This is because investment is equal to private and public savings (but assuming balanced budget public saving drops out so it would only be private savings I=S). This is because you can only invest what you save.

Moreover saving and consumption are mutually exclusive. From your income you can either consume or save there is no third option economically speaking (actually technically saving is postponed consumption but I don’t want to confuse you too much so I won’t go further into that).

Hence it’s quite intuitive that the more you consume, the less savings available and the higher the interest rate due to low savings and so on. 

So to sum up consumption must decrease investment as the more proportion of your income you consume the less you can save. If you consume 70% of your income you can only save 30%, if you consume 90% you can only save 10% and so on. If you consume 100% of your income your saving and thus investment is 0.