Hey can anyone Help me understand why this doesn't work and suggest a work around?

VF page:

<apex:page controller="paneltest">

    <apex:form >
    <apex:commandbutton action="{!settabpanel1}" value="tabcol1" rerender="outputpanel1,outputpanel2,outputpanel3"/>
    <apex:commandbutton action="{!settabpanel2}" value="tabcol2" rerender="outputpanel1,outputpanel2,outputpanel3"/>
    <apex:commandbutton action="{!settabpanel3}" value="tabcol3" rerender="outputpanel1,outputpanel2,outputpanel3"/>
    <apex:outputpanel rendered="{!showpanel1}" id="outputpanel1">
        Panel1
    </apex:outputpanel>
    <apex:outputpanel rendered="{!showpanel2}" id="outputpanel2">
        panel2
    </apex:outputpanel>
    <apex:outputpanel rendered="{!showpanel3}" id="outputpanel3">
        Panel3
    </apex:outputpanel>
</apex:form>
</apex:page>

Controller:

public class paneltest
{
    public boolean showpanel1 {get;set;}
    public boolean showpanel2 {get;set;}
    public boolean showpanel3 {get;set;}
    public boolean getShowpanel1()
    {
        return showpanel1;
    }
    public boolean getShowpanel2()
    {
        return showpanel2;
    }
    public boolean getShowpanel3()
    {
        return showpanel3;
    }
    public paneltest()
    {
        showpanel1=true;
        showpanel2=false;
        showpanel3=false;
    }
    public pagereference settabpanel1()
    {
        showpanel1=true;
        showpanel2=false;
        showpanel3=false;
        return null;
    }
    public pagereference settabpanel2()
    {
        showpanel1=false;
        showpanel2=true;
        showpanel3=false;
        return null;
    }
    public pagereference settabpanel3()
    {
        showpanel1=false;
        showpanel2=false;
        showpanel3=true;
        return null;

    }
 
}