Will I still owe taxes if I end the calendar year with a net loss on my brokerage account? I’ve made profitable trades and losing trades but my losses far exceed the gain

On the Sch D all your losses are netted against the gains  so if you have more losses you will have a capital loss to report on the 1040 and you are allowed to claim up to $3000 of loss against other income ... any loss you cannot use this year it carried forward and used next year. 

In other words, you can't use stock market losses to wipe out your income tax.