What causes the arising of fear that the sense of "me" will be threatened by the fruition of my practice? When practicing meditation (samatha and vipassana) intensely it feels like the sense of self is disintegrating and breaking apart. What causes that?
The Pali suttas teach self-identity is born from craving. For example:

The craving that makes for further becoming — accompanied by passion &amp;
delight, relishing now here &amp; now there — i.e., craving for sensual
pleasure, craving for becoming, craving for non-becoming: This, friend
Visakha, is the origination of self-identification described by the
Blessed One. MN 44
He assumes form to be a self. That assumption is a fabrication. Now
what is the cause, what is the origination, what is the birth, what is
the coming-into-existence of that fabrication? To an uninstructed,
run-of-the-mill person, touched by that which is felt born of contact
with ignorance, craving arises. That fabrication is born of that. SN
22.81
And what may be said to be subject to birth? Spouses &amp; children are
subject to birth. Men &amp; women slaves... goats &amp; sheep... fowl &amp;
pigs... elephants, cattle, horses &amp; mares... gold &amp; silver are
subject to birth. Subject to birth are these acquisitions, and one who
is tied to them, infatuated with them, who has totally fallen for
them, being subject to birth, seeks what is likewise subject to birth.
MN 26

From when you were very young, your mind attached to things due to both craving &amp; fear. For example, as a baby, your body was hungry and you attached to your mother, who was the source of food. Or when you were lonely &amp; frightened, you craved your mother's attention. Since your children, your life has probably continued like this. While you may not crave your mother for food &amp; comfort, you probably have sought pleasures &amp; attention from other things, so to escape the instinctual fear of being alone, bored &amp; restlessness. From these objects the mind craves &amp; attaches to, a sense of self-identity is born, such as: &quot;My mother, my toys, my food, my friends, my girlfriend, my boyfriend, my husband, my wife, my profession, my sport, my favourite pop star, my favourite movie, etc&quot;.
Meditation is similar to being alone. Because the sense of self-identity is built upon external attachments, the sense of self-identity can reduce &amp;/or break apart in meditation. What remains is the original fear the mind has been escaping since it was born into the world.
If your mind is naturally strong, you endure this fear until it passes. Even the Buddha did this, as described below:

So when fear &amp; terror came to me while I was walking back &amp; forth, I
would not stand or sit or lie down. I would keep walking back &amp; forth
until I had subdued that fear &amp; terror. When fear &amp; terror came to me
while I was standing, I would not walk or sit or lie down. I would
keep standing until I had subdued that fear &amp; terror. When fear &amp;
terror came to me while I was sitting, I would not lie down or stand
up or walk. I would keep sitting until I had subdued that fear &amp;
terror. When fear &amp; terror came to me while I was lying down, I would
not sit up or stand or walk. I would keep lying down until I had
subdued that fear &amp; terror. MN 4

However, there are meditators unable to endure this fear. For example, i listened to a Western monk of 30 years who has given up on even trying to overcome this fear. He spends most of his time as a monk talking &amp; teaching.
This lecture has a good introduction about what the 'self' is: Anattā and Rebirth
by Buddhadāsa Bhikkhu