SPSecurity.RunWithElevatedPrivileges(delegate()
{
    using(SPSite spSite = new SPSite(siteUrl))
    {
        using(SPWeb spWeb = spSite.OpenWeb())
        {
            spWeb.AllowUnsafeUpdates = true;
            for (int i =0; i < userRequest.Length; i++)
            {
                SPGroup spGroup = spWeb.SiteGroups[userRequest.GetValue(i).ToString() + "_Contribute"];
                spGroup.AddUser(selectedUser);  //this works just fine
            }
            try
            {
                SPGroupCollection userCollection = selectedUser.Groups;
                foreach(SPGroup group in userCollection)
                {
                    if(group.Name == spWeb.SiteGroups[userRequest.GetValue(i) + "_Read"].ToString())
                    {
                        group.RemoveUser(selectedUser); //this is where I get Access Denied and a catch in my method if the user is not a Site Admin when the code is ran
                    }
            }
            catch (Exception ex)
            {
                Console.WriteLine(ex.InnerException);
            }
        }
    }
});