The phrase "gives forth" refers to something that is released or emitted. The antonyms for "gives forth" would be to withhold, hold back, or contain. In this context, the opposite would be to keep something locked away or concealed, rather than to let it out for others to see or experience. For example, one might say that a secret or private thought is kept hidden and not given forth to others. Similarly, a news story or piece of information might be suppressed or withheld from the public, rather than being given forth for all to see.