Racism = Prejudice + Power. While racism can and does occur at the interpersonal level (using a slur, telling a joke, denying service, etc.), its more insidious and dangerous forms are institutional and ideological. Check out The Four I's of Oppressionto learn about the many manifestations of racism.
But I'm not a racist! Of course you don't do racist things like use derogatory slurs, but if you have racial privilege it's highly likely you accidentally engage in more covert and subconscious forms of racism, like aversive racism, othering, micro-aggressions. But I'm a woman/I grew up poor/I have a disability, so I don't have privilege! Having racial privilege doesn't mean your life hasn't been hard, but people with racial privilege benefit from systemic racism whether they like it or not. Even if you grew up poor, disabled, or suffered in other ways, if you are white then you didn't have the added burden of racism on top of your other challenges- that's White Privilege. Check out the Privilege Checklist and see how it makes you feel. The defensiveness many people feel is explained by a concept called White Fragility.
I feel awful. Make it stop. Many white folks resist learning about racism because it makes us feel guilty, ashamed, and worse. But doing nothing won't make these feelings go away and it certainly won't dismantle racism. You can feel better by becoming part of the solution. Check out the Equity Mindset Course Series to get started.