And yes, Jesus does teach us to love as he loves. From a Calvinist point of view, this is possible for those who have been regenerated because as I quoted above from the Westminster Confession:
VII. Neither are the forementioned uses of the law contrary to the grace of the Gospel, but do sweetly comply with it; the Spirit of Christ subduing and enabling the will of man to do that freely, and cheerfully, which the will of God, revealed in the law, requires to be done.
Chapter 13, the Confession speaks to the reality of sanctification and growth in grace by the power of the Holy Spirit:
I. They, who are once effectually called, and regenerated, having a new heart, and a new spirit created in them, are further sanctified, really and personally, through the virtue of Christ’s death and resurrection, by His Word and Spirit dwelling in them: the dominion of the whole body of sin is destroyed, and the several lusts thereof are more and more weakened and mortified; and they more and more quickened and strengthened in all saving graces, to the practice of true holiness, without which no man shall see the Lord.
II. This sanctification is throughout, in the whole man; yet imperfect in this life, there abiding still some remnants of corruption in every part; whence arises a continual and irreconcilable war, the flesh lusting against the Spirit, and the Spirit against the flesh.
III. In which war, although the remaining corruption, for a time, may much prevail; yet, through the continual supply of strength from the sanctifying Spirit of Christ, the regenerate part does overcome; and so, the saints grow in grace, perfecting holiness in the fear of God.