Like others, I do not accept the premise that religions (or any ideologies for that matter) are the root source of human hatred. It seems to me the root source of human hatred is a fundamental property of the universe: diversity. By "diversity" I mean that the universe is composed of individual things that are different from one another in time, space, and nature. These individual things then have different interactions and relationships with each other. Those interactions take many forms and have many outcomes. Inevitably, some of those interactions will be adversarial. Conflict is an inherent consequence of the universe being diverse and full of individual things that can have relationships. In humans, hatred is a specific type of response resulting from diversity - an emotional one brewed from adversarial relationships.
There's another ingredient that seems key to producing hatred in humans, though. That ingredient is intolerance. In order to hate, one has to have drawn a line and settled upon some particular way of being, thinking, or doing. When one is set in one's ways, if some diverse element of the universe comes along and upsets those ways, that adversity then upsets us. We can tolerate a certain amount of friction and upset, but beyond that line, the tolerance becomes intolerance. The "I can manage this" becomes "I can't deal with this" and the human animal goes on fight or flight mode. Hatred and fear, consequential cousins, both emerge when our backs are against the wall.
Religion encompasses so much of a person's identity that it's a particularly ripe source of conflicts between diverse groups. Doubly so as religions are a tremendous source of diversity in human culture. As such, it's difficult to fault some atheists for pointing a finger at religions as a source of hatred. Still, I don't think that finger pointing is useful. It misses the underlying cause - diversity itself - to fault a particular type of diversity. Personally, I can't finger religions while ignoring how differences in skin color, sex and gender, romantic orientation, socioeconomic status, political allegiances, and so forth also spawn hatred.