It can go either way.
When the police "have a hard on" for someone, it means they're looking to put that person in jail.
But it can mean approval as well.
Consider this line from Stanley Kubrick's film Full Metal Jacket : Gunnery Sergeant Hartman: Today ... is Christmas!
There will be a magic show at zero-nine-thirty!
Chaplain Charlie will tell you about how the free world will conquer Communism with the aid of God and a few Marines!
God has a hard-on for Marines because we kill everything we see!
He plays His games, we play ours!
To show our appreciation for so much power, we keep heaven packed with fresh souls!
God was here before the Marine Corps!
So you can give your heart to Jesus, but your ass belongs to the Corps!
Do you ladies understand?
Clearly, Sgt.
Hartman means that God likes Marines when he uses this expression.
english.stackexchange.com/users/2303/Robusto
It can mean that they have a grudge and are actively trying to settle it, which would often include aggressive or belligerent behavior.
I think the meaning comes from a general sense of being focused on someone to a degree reminiscent of sexual fascination.
english.stackexchange.com/users/4526/chaos
I suggest that the shared concept is being aroused , sexually or some other way.
Sexual Arousal : The directly biological sexual form.
(Discretion suggests I not provide an example.)
Aggressive Arousal : A person can have a hard on in an aggressive, competitive manner, as the accepted answer suggests.
Testosterone can fuel both sexual and aggressive arousal, so there's a biological link.
"Bob had a real hard on for Dave's job."
Broadly Desirous Arousal : A person can also have a hard on for anything desirable: a new videogame, a new model of car, even eating at a particular restaurant.
"Bob had a serious hard on for the Tesla Roadster.
" (None of the existing answers included the general concept of arousal
so I figured I'd add one.)
english.stackexchange.com/users/2969/Matthew Frederick
Well, it's a clearly sexual term, but I've never heard it used in an aggressive sense.
When used non-sexually, it generally would indicate that someone really likes something (or someone) and is inclined to talk it up at any opportunity.
There's also a connotation that they're rather obnoxiously persistent about doing so.
english.stackexchange.com/users/2490/Hellion
I've heard the phrase used in a corporate setting to describe someone who is aggressively focused on surpassing or doing down a particular rival, or on defeating a project or proposal.
In this usage, I believe that deploying a phrase with sexual significance is a kind of intensifier, because the speaker is juxtaposing that significance on such a non-sexual context.
english.stackexchange.com/users/3952/Tom Hughes
I believe that there are two somewhat similar expressions to using the term "hard on."
Only one of them has a sexual connotation.
To BE "hard on
" somebody is to be tough or difficult with them.
This can come from either a man or a woman.
It often refers to "aggression" but has no sexual connotation.
To HAVE a "hard on" is for a man's particular body part to have a certain "hardness" (when it is more often "soft" or "limp".)
And that takes place in a sexual context.
english.stackexchange.com/users/10287/Tom Au
What does it mean to "have a hard-on for someone" in a non-sexual sense? I've heard it used in contexts that make it seem like the subject is acting aggressive or belligerent toward "someone". Is that right?
Non-sexual meaning of "to have a hard-on for someone"
english.stackexchange.com
<meaning><american-english><slang><offensive-language>
english.stackexchange.com/questions/12148
english.stackexchange.com/users/3591/Nick
There are number of potential non sexual meanings for the phrase "have a hard-on for someone" and the exact answer will depend on context. One example is that, when the police "have a hard-on" for someone, it means they're looking to put them in jail. It can also mean that someone has a grudge or that they really like something (or someone). This phrase could also refer to someone who is aggressively focused on surpassing or doing down a particular rival. In policing, it is a term to mean the police are looking for someone. It can also mean someone is actively seeking to settle a grudge and is particularly aggressive. The focus on intent is so strong that it is the equivalent of sexual interest. The other plain meaning is sexual arousal, but also being aroused in some way. In some cases the person is aggressive as testosterone and male arousal are linked.. If the term was implied non-sexually, it would mean a strong interest in something. It has been used in corporate settings to denote aggressive determination to win or achieve something, but with an undertone of obnoxious-type behaviour
There are number of potential non sexual meanings for the phrase "have a hard-on for someone" and the exact answer will depend on context. One example is that, when the police "have a hard-on" for someone, it means they're looking to put them in jail. It can also mean that someone has a grudge or that they really like something (or someone). This phrase could also refer to someone who is aggressively focused on surpassing or doing down a particular rival. When used in a non-sexual way, the term generally means intense focus on something or desire for something. It is probable that the sexual connotation is intended in these cases, either as a metaphor or an intensifier.
The expression 'to have a hard-on for someone' can possibly have some non sexual meanings. It generally would indicate that someone really likes something (or someone) and is inclined to talk it up at any opportunity.  It can mean that someone has a grudge and are actively trying to settle it, which would often include aggressive or belligerent behavior. Also it can be used in a corporate setting to describe someone who is aggressively focused on surpassing or doing down a particular rival, or on defeating a project or proposal. It can be used by the police meaning they're looking to put that person in jail.   The mean of this phrase is open to interpretation and some people may not have heard it in a non-sexual sense. It could imply that someone is aggressively trying to catch or surpass someone, or it could indicate a strong liking for someone or something.
Sexual Arousal : The directly biological sexual form.
Sexual Arousal : The directly biological sexual form.
A policing term Having a grudge and are actively trying to settle it, involvingaggressive or belligerent behavior.   Sexual arousal or another type of strong arousal. Being aggressively aroused with a strong intention Corporate use to denote drive and determination.
When used in a non-sexual way, the term generally means intense focus on something or desire for something. It is probable that the sexual connotation is intended in these cases, either as a metaphor or an intensifier.
The meaning of this phrase is open to interpretation. This phrase could mean that someone is aggressively trying to catch or surpass someone. When used non-sexually, this phrase could indicate a liking for someone or something. Some people may not have heard this phrase used in a non-sexual sense.