The most likely reason your comparator won’t output high properly is that it has an open collector or open drain output scheme. As an example, take a look at the functional block diagram in the datasheet of AS393AMTR-G1DITR-ND.
This device has an open collector output, which requires a pull-up resistor at its output to be able to output a high state (the same is true if it were open drain). Other integrated circuit outputs for devices other than comparators can have the same open collector/drain style, always check a part’s datasheet for details.
For more detailed explanations of open collector and open drain see: