(CNN) The father of a man killed in a case highlighting Florida's "stand your ground" law called Thursday for the shooter to be prosecuted, saying his son was rightly standing up for his family and that there's no way the shooting could be justified.

Markeis McGlockton was shot and killed July 19 outside a convenience store in Clearwater by Michael Drejka, sheriff's detectives say, after McGlockton shoved Drejka to the ground for confronting McGlockton's girlfriend over a parking space.

Drejka was not arrested, with the Pinellas County sheriff saying the "stand your ground" law appears to give him immunity because he feared a further attack.

McGlockton's father said he raised his son to be a man who could protect his family, and "that's all my son was doing."

"If you push a man down to the ground, that man does not deserve to be shot. Stand up and fight with your fists," Michael McGlockton said at a news conference in front of the Pinellas County Justice Center in Clearwater.

The father joined his son's girlfriend and their lawyers, including civil rights attorney Benjamin Crump, in calling for Drejka's prosecution.

Britany Jacobs, Markeis McGlockton's girlfriend of nine years, said she is having trouble explaining his death to their older children, ages 5 and 3. They also have a 4-month-old.

"They asked me where is their daddy, and I need answers, because it's hard for me to even say where the father is right now," said Jacobs, 25.

Michael McGlockton speaks about the death of his son, Markeis McGlockton, Thursday in Clearwater, Florida. Behind him is attorney Benjamin Crump; at left is Markeis' girlfriend, Britany Jacobs.

The confrontation

Sheriff's detectives said Drejka, 47, approached Jacobs while McGlockton and the couple's 5-year-old son went into the store. Drejka and Jacobs began arguing about her parking in a handicapped parking space.

Jacobs concedes she parked in a handicapped spot outside the Circle A Food Store in Clearwater, and told "Good Morning America" this week that Drejka pulled up in a silver SUV and began yelling and cursing at her.

"(McGlockton) comes out and sees a guy yelling at me and I'm sitting in the car. So, by this time, my man is defending me and defending his children so he pushes the guy down," she told the ABC show

Jacobs said her two younger children were in the car with her.

Surveillance footage from the store shows McGlockton exit the Circle A and make a beeline for Drejka, whom he shoves upon reaching him. Drejka tumbles back onto his butt as McGlockton briefly stands over him, pulling up his shorts.

Surveillance footage captured the altercation between McGlockton and Drejka.

Drejka pulls out a gun and McGlockton steps back and quickly clutches his chest before running back into the store and collapsing in front of his son. There is no sound on the video, but the Pinellas County Sheriff's Office said in a news release , "Witnesses told detectives that Drejka was on the ground when he took out a handgun and fired one single round at McGlockton, striking him in the chest."

The time between Drejka hitting the ground and the shooting was four to five seconds, authorities have said.

Sheriff Bob Gualtieri said Florida's "stand your ground" law prevented him from arresting Drejka, because McGlockton violently shoved him and Drejka feared further harm.

Florida's law says someone is justified in using deadly force if he or she reasonably believes it is necessary to prevent imminent death or great bodily harm, or to prevent a forcible felony. And, the law says, the person using deadly force does not have to retreat if he or she "is not engaged in a criminal activity and is in a place where he or she has a right to be."

Gualtieri said the county's state attorney would consider the case.

"If he concurs, there will be no arrest," Gualtieri said.

Drejka was cooperative with deputies and has a valid Florida concealed weapons license, the sheriff's office said.

Repeated attempts to reach Drejka have been unsuccessful. CNN affiliate WFTS reported that the 47-year-old put a sign outside his home that read, "No comment."

Crump: Race is a factor in this case

Crump said he believes that "stand your ground" is being applied to the wrong person in this case. He contends Drejka was the initial aggressor by starting the argument with Jacobs.

"You cannot provoke a fight and then hide behind 'stand your ground,'" Michele Rayner, another attorney representing McGlockton's family, said Thursday.

JUST WATCHED Victim's girlfriend: He didn't have to go like this Replay More Videos ... MUST WATCH Victim's girlfriend: He didn't have to go like this 02:33

Crump contends race is a factor in the case. McGlockton was -- and Jacobs and their children are -- black.

"Just imagine if the roles were reversed, and you had a black man approach a white woman sitting in the car with her two white toddler children in the back seat, and the white father came out to protect his family," Crump said, adding he believed the black man would be arrested in that scenario.

"So why is it different when there is an unarmed black person lying on the ground dead? We only want equal justice -- nothing more, but nothing less," Crump said.

Gualtieri has defended Drejka, describing McGlockton's push as forcible and violent.

He said there's no evidence Drejka posed a threat to McGlockton's family. It was strictly a verbal argument and McGlockton engaged in unlawful conduct by pushing Drejka, the sheriff said during a news conference last week.

"Markeis wouldn't be dead if Markeis didn't slam this guy to the ground," Gualtieri said.

Gualtieri also noted the framework of Florida's "stand your ground" law was changed this year.

Previously, a shooter who used "stand your ground" as a defense had to prove she or he feared further bodily harm. The law now says the state attorney has to provide "clear and convincing evidence" the shooter is not entitled to "stand your ground" immunities.

A community is angry

Mourners and protesters gathered Sunday night for a church vigil before marching more than a mile to the Circle A Food Store. Local news footage from the march showed demonstrators carrying signs that read, "He was murdered in front of his kids" and "Indict Drejka! The whole system is guilty."

Some protesters called for the repeal of "stand your ground," claiming it was racist in its application. Crump concurred in a CNN interview on Tuesday, calling the law "a license to kill black people and people of color and not be held accountable."

"The state attorney needs to make sure this cold-blooded murderer does not get away with this," Crump said. "It's the law, and it's ludicrous. It's just a very bad law that encourages people in society to take the laws into their own hands."